-edge magic total labelingfor the extended duplicate graph of quadrilateral snake Z 3. -vertex magic total labeling and Z 3
|
|
- Christiana McDonald
- 5 years ago
- Views:
Transcription
1 Journal of Physics: Conference Series PAPER OPEN ACCESS Z 3 -vertex magic total labeling and Z 3 -edge magic total labelingfor the extended duplicate graph of quadrilateral snake Related content - E-cordial and product e-cordial labeling for the extended duplicate graph of splitting graph of path R. Avudainayaki, B. Selvam and P.P. Ulaganathan To cite this article: P Indira et al 2018 J. Phys.: Conf. Ser View the article online for updates and enhancements. This content was downloaded from IP address on 03/11/2018 at 11:58
2 Z 3 -vertex magic total labeling and Z 3 -edge magic total labelingfor the extended duplicate graph of quadrilateral snake P Indira 1, B Selvam 2, K Thirusangu 2 1 Department of Mathematics, St.Thomas College of Arts& Science,Chennai Department of Mathematics, S.I.V.E.T. College, Gowrivakkam, Chennai indu-sel@yahoo.in, kbmselvam@gmail.com, kthirusangu@gmail.com Abstract. Based on the works of Kotzig, Rosa and MacDougall et.al., we present algorithms and prove the existence of Z 3 -vertex magic total labeling and Z 3 -edge magic total labeling for the extended duplicate graph of quadrilateral snake. 1. Introduction The concept of graph labeling was introduced by Rosa in Kotzig and Rosa [2] defined the concept of edge magic total labeling. In 1999, MacDougall et.al [4] investigated the idea of vertex magic total labeling. A detailed study on graph labeling has been done by Gallian[1]. E.Sampthkumar [3] introduced the concept of duplicate graph. The idea of extended duplicate graph was introduced by K.Thirusangu, B.Selvam and P.Ulaganathan [5] and they have proved that the existence of cordial labeling for the EDG of twig graphs. J. BaskarBabujee and L.Shobana [6] discussed on Z 3 -Magic Labeling for Cayley Digraphs. E.Bala andk.thirusangu [7] studied on E- Cordial and Z 3 -Magic labeling for the extended triplicate graph of a path. 2. Preliminaries First, we will give some brief summary of definitions which are related to this paper. Definition 2.1 : A quadrilateral Snake QS m is obtained from a path u 1, u 2, u 3,, u n by joining u i and u i+1 to two new vertex v i and w i respectively and then joining v i and w i, 1 i n-1, where m is the number of edges of the path. In general, a quadrilateral snake has 3m+1 vertices and 4m edges. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd 1
3 Definition 2.2 : Let G (V,E) be a graph and the duplicate graph of G is (V 1, E 1 ) where V 1 is the union of V and V and intersection of V and V is and E 1 is defined as the edge ab is in E if and only if both ab and a b are edges in E 1. Definition 2.3 : Extended duplicate graph of quadrilateral snake is obtained by adding the edge v 2 v 2 to the duplicate graph. It is denoted by EDG(QS m ) and it has 6m+2 vertices and 8m+1 edges, where m is the number of edges. Definition 2.4 : We call a function f is Z 3 - vertex magic total labeling of a graph G, if f: V Ս E A* where A* = Z 3 {0} in such a way that the induced function f* on V is f*(v i ) = {f(v i ) + Σf(uv i )}(mod 3) = k, a constant for all edges uv i ϵ E. Definition 2.5 : We call a function f is Z 3 - edge magic total labelingof a graph G, if f: V Ս E A* where A* = Z 3 {0} in such a way that the induced function f* on E is f* (v i v j ) = { f(v i ) + f(v j ) + f(v i v j )} (mod 3) = k, a constant for all edges v i v j ϵ E. 3. Main Results 3.1. Z 3 -vertex magic total labeling In this section, we present algorithm and prove the existence of Z 3 - vertex magic total labeling for EDG(QS m ). Algorithm: 1 V {v 1,v 2,v 3,,v 3m,v 3m+1, v 1,v 2,v 3,.,v 3m,v 3m+1 } E {e 1,e 2,e 3,e 4m, e 4m+1,e 1,e 2,e 3,e 4m } v 1, 1,v 1 1, v 2 2, v 2 2, e 4m+1 2 // assignment of labels to the vertices and edges of EDG(QS m ) for i = 0 to (m-1) do v 3+3i 1 v 4+3i 2 v 3+3i 2 v 4+3i 1 for i = 0 to (m-2) do v 5+3i 1 v 5+3i 1 for i = 0 to (m-1) do for j= 0 to 1 e 1+2j+4i 1 e 1+2j+4i 2 fori=0 to (m-1) do e 2+4i 2 2
4 e 4+4i 1 e e 4+4i 1 end procedure Theorem 1 : The EDG [QS m ], m 1 admits Z 3 - vertex magic total labeling. Proof: Let EDG(QS m ) be the extended duplicate graph of quadrilateral snake. Defining the set of vertices and edges are V(G) = {v 1, v 2,,v 3m, v 3m+1, v 1, v 2,..., v 3m, v 3m 1} E(G) = {e 1, e 2,,e 4m, e 4m+1, e 1, e 2,..., e 4m } Define a function f : V E {1, 2} as given in algorithm 1. Then the vertices and edges are labeled as follows: The vertices v 1 and v 1 receive label 1 and the vertices v 2 and v 2 receive label 2. For i = 0 to (m-1), the vertices v 3+3i receive label 1 ; the vertices v 4+3i receive label 2 ; the vertices v 4+3i receive label 1 ; the vertices v 3+3i receive label 2. For i = 0 to (m-2), the vertices v 5+3i receive label 1 ; the vertices v 5+3i receive label 1. The edge e 3m+1 receive label 2. For 0 i (m-1) and 0 j 1, the edges e 1+2j+4i receive label 1 and the edges e 1+2j+4i receive label 2. For 0 i (m-1), the edges e 4+4i receive label 1, the edges e 2+4i receive label 2, the edges e 4+4i receive label 1 and the edges e 2+4i receive label 1. Thus the entire 6m+2 vertices and 8m+1 edges are labeled. The induced function f * :E {1,2} is defined as f * (v i ) = { f (v i ) + f (uv i )} (mod 3) = k, a constant for all edges uv i E. Therefore the induced function yields Z 3 -vertex magic total labeling as a constant 1. Hence the EDG of quadrilateral snake graph QS m, m 1 admits Z 3 vertex magic total labeling. Illustration 1: A graph and its Z 3 - vertex magic total labelling EDG(QS 4 ) 3
5 3.2. Z 3 edge magic total labeling In this section, we present algorithm and prove the existence of Z 3 edge magic total labeling for EDG(QS m ). Algorithm: 2 V {v 1,v 2,v 3,,v 3m,v 3m+1, v 1,v 2,v 3,.,v 3m,v 3m+1 } E {e 1,e 2,e 3,e 4m, e 4m+1,e 1,e 2,e 3,e 4m } v 1 1,v 1 1, e 3m+1 1 // assignment of labels to the vertices and edges of EDG(QS m ) for i = 1 to 4m do e i 1, e i 1 for i = 0 to [(m-1)/2] do v 2+6i 2 v 3+6i 1 v 4+6i 2 v 2+3i 2 v 3+6i 1 v 4+6i 2 4
6 for i = 0 to [(m-2)/2] do v 5+6i 2 v 6+6i 1 v 7+6i 2 v 5+3i 2 v 6+6i 1 v 7+6i 2 end procedure Theorem 2 : EDG [QS m ], m 1 admits Z 3 - edge magic total labeling. Proof: Let EDG(QS m ) be the extended duplicate graph of quadrilateral snake. Defining set of vertices and edges are V(G) = {v 1, v 2,,v 3m, v 3m+1, v 1, v 2,..., v 3m, v 3m 1} E(G) = {e 1, e 2,,e 4m, e 4m+1, e 1, e 2,..., e 4m } To label the vertices and edges, define a function f : V E {1, 2} as given in algorithm 2. Then the vertices and edges are labeled as follows: The vertices v 1 and v 1 receive label 1. For 0 i [(m-1)/2], the vertices v 2+6i receive label 2 ; the vertices v 3+6i receive label 1 ; the vertices v 4+6i receive label 2 ; the vertices v 2+6i receive label 2 ; the vertices v 3+6i receive label 1 and the vertices v 4+6i receive label 2 ; For 0 i [(m-2)/2], the vertices v 5+6i receive label 2 ; the vertices v 6+6i receive label 1 ; the vertices v 7+6i receive label 2 ; the vertices v 5+6i receive label 2 ; the vertices v 6+6i receive label 1 and the vertices v 7+6i receive label 2. The edge e 3m+1 receive label 1. For 0 i 4m, the edges e i and e i receive label 2. Thus, the entire 6m+2 vertices and 8m+1 edges are labeled. The induced function f* : E {1, 2} is defined as f *(v i v j ) = { f (v i )+ f (v j )+f (v i v j )} (mod 3) = k, a constant for all edges v i v j E. The induced function yields Z 3 -edge magic total labeling as a magic constant 2. Hence the EDG of quadrilateral snake graph QS m, m 1 admits Z 3 edge magic total labeling. Illustration 2: A graph and its Z 3 -edge magic total labelling EDG(QS 4 ) 5
7 4. Conclusion Here we have constructed algorithms and proved that the extended duplicate graph(edg) of quadrilateral snake graph(qs m ) admits Z 3 vertex magic total labeling and Z 3 edge magic total labeling. References [1] Gallian J A 2015 A Dynamic Survey of graph labeling the Electronic Journal of combinatorics19# DS6 [2] Kotzig A and Rosa A 1970 Magic valuations of finite graphs Canad.math.Bull
8 [3] Sampath kumar E 1973 On duplicate graphs Journal of the Indian Math. Soc [4] Macdougall J A, Mirka Miller and wallis W D 2002 Vertex-magic total labeling of wheels and related graphs Utilitas mathematica [5] Thirusangu K, Selvam B and Ulaganathan P P 2010 Cordial labeling for the extended duplicate twig graphs International Journal of computer, mathematical sciences and applications4(3 4) [6] Baskar Babujee J and Shobana L 2010 On Z3-Magic Labeling and Cayley Digraphs Int. J. Contemp. Math. Sciences5(48) [7] Bala E and Thirusangu K 2011 E-Cordial and Z3-Magic Labelings in Extended Triplicate Graph of a Path Gen. Math. Notes5(2)
Total magic cordial labeling and square sum total magic cordial labeling in extended duplicate graph of triangular snake
2016; 2(4): 238-242 ISSN Print: 2394-7500 ISSN Online: 2394-5869 Impact Factor: 5.2 IJAR 2016; 2(4): 238-242 www.allresearchjournal.com Received: 28-02-2016 Accepted: 29-03-2016 B Selvam K Thirusangu P
More informationSigned Product Cordial labeling in duplicate graphs of Bistar, Double Star and Triangular Ladder Graph
Signed Product Cordial labeling in duplicate graphs of Bistar Double Star Triangular Ladder Graph P.P Ulaganathan #1 B. Selvam #2 P. Vijaya kumar #3 12 Department of Mathematics S.I.V.E.T College Gowrivakkam
More informationSome Cordial Labeling of Duplicate Graph of Ladder Graph
Annals of Pure and Applied Mathematics Vol. 8, No. 2, 2014, 43-50 ISSN: 2279-087X (P), 2279-0888(online) Published on 17 December 2014 www.researchmathsci.org Annals of Some Cordial Labeling of Duplicate
More informationSOME GRAPHS WITH n- EDGE MAGIC LABELING
SOME GRAPHS WITH n- EDGE MAGIC LABELING Neelam Kumari 1, Seema Mehra 2 Department of mathematics, M. D. University Rohtak (Haryana), India Abstract: In this paper a new labeling known as n-edge magic labeling
More informationGraceful Labeling for Some Star Related Graphs
International Mathematical Forum, Vol. 9, 2014, no. 26, 1289-1293 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.4477 Graceful Labeling for Some Star Related Graphs V. J. Kaneria, M.
More informationON SOME LABELINGS OF LINE GRAPH OF BARBELL GRAPH
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 10 017, 148 156 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu ON SOME LABELINGS
More informationSOME RESULTS ON n-edge MAGIC LABELING part 2
International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April-2016 1453 SOME RESULTS ON n-edge MAGIC LABELING part 2 S.Vimala, Assistant Professor, Department of Mathematics, Mother
More informationPrime and Prime Cordial Labeling for Some Special Graphs
Int. J. Contemp. Math. Sciences, Vol. 5, 2, no. 47, 2347-2356 Prime and Prime Cordial Labeling for Some Special Graphs J. Baskar Babujee and L. Shobana Department of Mathematics Anna University Chennai,
More informationAMO - Advanced Modeling and Optimization, Volume 16, Number 2, 2014 PRODUCT CORDIAL LABELING FOR SOME BISTAR RELATED GRAPHS
AMO - Advanced Modeling and Optimization, Volume 6, Number, 4 PRODUCT CORDIAL LABELING FOR SOME BISTAR RELATED GRAPHS S K Vaidya Department of Mathematics, Saurashtra University, Rajkot-6 5, GUJARAT (INDIA).
More informationInternational Journal of Mathematics Trends and Technology (IJMTT) Special Issue NCCFQET May 2018
Acyclic Coloring of Middle and Total graph of Extended Duplicate graph of Ladder Graph C. Shobana Sarma 1, K. Thirusangu 2 1 Department of Mathematics, Bharathi Women s College (Autonomous) Chennai 600
More informationEVEN SUM CORDIAL LABELING FOR SOME NEW GRAPHS
International Journal of Mechanical ngineering and Technology (IJMT) Volume 9, Issue 2, February 2018, pp. 214 220 Article ID: IJMT_09_02_021 Available online at http://www.iaeme.com/ijmt/issues.asp?jtype=ijmt&vtype=9&itype=2
More informationNEIGHBOURHOOD SUM CORDIAL LABELING OF GRAPHS
NEIGHBOURHOOD SUM CORDIAL LABELING OF GRAPHS A. Muthaiyan # and G. Bhuvaneswari * Department of Mathematics, Government Arts and Science College, Veppanthattai, Perambalur - 66, Tamil Nadu, India. P.G.
More informationProduct Cordial Labeling of Some Cycle Related Graphs
Product Cordial Labeling of Some Cycle Related Graphs A. H. Rokad 1, G. V. Ghodasara 2 1 PhD Scholar, School of Science, RK University, Rajkot - 360020, Gujarat, India 2 H. & H. B. Kotak Institute of Science,
More informationVERTEX ODD DIVISOR CORDIAL GRAPHS
Asia Pacific Journal of Research Vol: I. Issue XXXII, October 20 VERTEX ODD DIVISOR CORDIAL GRAPHS A. Muthaiyan and 2 P. Pugalenthi Assistant Professor, P.G. and Research Department of Mathematics, Govt.
More informationGraceful Labeling for Cycle of Graphs
International Journal of Mathematics Research. ISSN 0976-5840 Volume 6, Number (014), pp. 173 178 International Research Publication House http://www.irphouse.com Graceful Labeling for Cycle of Graphs
More informationOn Cordial Labeling: Gluing of Paths and Quadrilateral Snake Graphs on Cycle Graph
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 12, Number 4 (2016), pp. 3559 3567 Research India Publications http://www.ripublication.com/gjpam.htm On Cordial Labeling: Gluing of
More informationProduct Cordial Labeling for Some New Graphs
www.ccsenet.org/jmr Journal of Mathematics Research Vol. 3, No. ; May 011 Product Cordial Labeling for Some New Graphs S K Vaidya (Corresponding author) Department of Mathematics, Saurashtra University
More informationPAijpam.eu PRIME CORDIAL LABELING OF THE GRAPHS RELATED TO CYCLE WITH ONE CHORD, TWIN CHORDS AND TRIANGLE G.V. Ghodasara 1, J.P.
International Journal of Pure and Applied Mathematics Volume 89 No. 1 2013, 79-87 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v89i1.9
More informationTOTAL SEQUENTIAL CORDIAL LABELING OF UNDIRECTED GRAPHS
National Journal on Advances in Computing & Management Vol. 4 No. 2 Oct 2013 9 TOTAL SEQUENTIAL CORDIAL LABELING OF UNDIRECTED GRAPHS Parameswari.R 1, Rajeswari.R 2 1 Research Scholar,Sathyabama University,
More informationSeema Mehra, Neelam Kumari Department of Mathematics Maharishi Dayanand University Rohtak (Haryana), India
International Journal of Scientific & Engineering Research, Volume 5, Issue 10, October-014 119 ISSN 9-5518 Some New Families of Total Vertex Product Cordial Labeling Of Graphs Seema Mehra, Neelam Kumari
More informationPrime Harmonious Labeling of Some New Graphs
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 12, Issue 5 Ver. IV (Sep. - Oct.2016), PP 57-61 www.iosrjournals.org Prime Harmonious Labeling of Some New Graphs P.Deepa
More informationCycle Related Subset Cordial Graphs
International Journal of Applied Graph Theory Vol., No. (27), 6-33. ISSN(Online) : 2456 7884 Cycle Related Subset Cordial Graphs D. K. Nathan and K. Nagarajan PG and Research Department of Mathematics
More informationGraceful and odd graceful labeling of graphs
International Journal of Mathematics and Soft Computing Vol.6, No.2. (2016), 13-19. ISSN Print : 2249 3328 ISSN Online: 2319 5215 Graceful and odd graceful labeling of graphs Department of Mathematics
More informationHeronian Mean Labeling of Graphs
International Mathematical Forum, Vol. 12, 2017, no. 15, 705-713 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.68108 Heronian Mean Labeling of Graphs S.S. Sandhya Department of Mathematics
More informationVertex Odd Divisor Cordial Labeling for Vertex Switching of Special Graphs
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (017), pp. 555 5538 Research India Publications http://www.ripublication.com/gjpam.htm Vertex Odd Divisor Cordial Labeling
More informationGracefulness of a New Class from Copies of kc 4 P 2n and P 2 * nc 3
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 2, Number 1 (2012), pp. 75-81 Research India Publications http://www.ripublication.com Gracefulness of a New Class from Copies
More informationSquare Difference Prime Labeling for Some Snake Graphs
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 3 (017), pp. 1083-1089 Research India Publications http://www.ripublication.com Square Difference Prime Labeling for Some
More informationVariation of Graceful Labeling on Disjoint Union of two Subdivided Shell Graphs
Annals of Pure and Applied Mathematics Vol. 8, No., 014, 19-5 ISSN: 79-087X (P), 79-0888(online) Published on 17 December 014 www.researchmathsci.org Annals of Variation of Graceful Labeling on Disjoint
More informationAnalysis of Some Bistar Related MMD Graphs
Volume 118 No. 10 2018, 407-413 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v118i10.41 ijpam.eu Analysis of Some Bistar Related MMD
More informationDivisor Cordial Labeling in the Context of Graph Operations on Bistar
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 12, Number 3 (2016), pp. 2605 2618 Research India Publications http://www.ripublication.com/gjpam.htm Divisor Cordial Labeling in the
More informationPrime Labeling for Some Cycle Related Graphs
Journal of Mathematics Research ISSN: 1916-9795 Prime Labeling for Some Cycle Related Graphs S K Vaidya (Corresponding author) Department of Mathematics, Saurashtra University Rajkot 360 005, Gujarat,
More informationConstruction of Some (n,m) Petersen Graphs. with Vertex Magic Total Labeling
Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 4, 153-158 Construction of Some (n,m) Petersen Graphs with Vertex Magic Total Labeling R. Senthil Amutha Department of Mathematics Sree Saraswathi Thyagaraja
More informationSuper vertex Gracefulness of Some Special Graphs
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 11, Issue 3 Ver. V (May - Jun. 2015), PP 07-15 www.iosrjournals.org Super vertex Gracefulness of Some Special Graphs N.Murugesan
More informationDivisor cordial labeling in context of ring sum of graphs
International Journal of Mathematics and Soft Computing Vol.7, No.1 (2017), 23-31. ISSN Print : 2249-3328 ISSN Online : 2319-5215 Divisor cordial labeling in context of ring sum of graphs G. V. Ghodasara
More informationMore on Permutation Labeling of Graphs
International Journal of Applied Graph Theory Vol.1, No. (017), 30-4. ISSN(Online) : 456 7884 More on Permutation Labeling of Graphs G. V. Ghodasara Department of Mathematics H. & H. B. Kotak Institute
More informationInternational Journal of Mathematics Trends and Technology (IJMTT) Volume 36 Number 4- August 2016
Vertex Bimagic Total Labeling for Graphs R. Senthil Amutha 1, N. Murugesan 2 1 Department of Mathematics, Sree Saraswathi Thyagaraja College, Pollachi, India 2 Department of Mathematics, Government Arts
More informationPrime Labeling for Some Planter Related Graphs
International Journal of Mathematics Research. ISSN 0976-5840 Volume 8, Number 3 (2016), pp. 221-231 International Research Publication House http://www.irphouse.com Prime Labeling for Some Planter Related
More informationODD VERTEX MAGIC TOTAL LABELING OF TREES CT. NAGARAJ#1,C.Y. PONNAPPAN?1, G. PRABAKARAN#2 1
ODD VERTEX MAGIC TOTAL LABELING OF TREES CT NAGARAJ#1,CY ONNAAN?1, G RABAKARAN# 1 Research Scholar, Department of Mathematics Research and Development centre Bharathiar University, Coimbatore-641046, Tamilnadu,
More informationHeronian Mean Labeling of. Disconnected Graphs
International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 5, 201-208 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.6841 Heronian Mean Labeling of Disconnected Graphs
More informationGraph Labelings in Konigsberg Bridge Problem
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 11, Issue 5 Ver. II (Sep. - Oct. 2015), PP 29-36 www.iosrjournals.org Graph Labelings in Konigsberg Bridge Problem N.
More informationOdd Harmonious Labeling of Some Graphs
International J.Math. Combin. Vol.3(0), 05- Odd Harmonious Labeling of Some Graphs S.K.Vaidya (Saurashtra University, Rajkot - 360005, Gujarat, India) N.H.Shah (Government Polytechnic, Rajkot - 360003,
More informationEdge-Odd Graceful Labeling for Sum of a Path and a Finite Path
Global Journal of Mathematical Sciences: Theory and Practical. ISSN 0974-3200 Volume 9, Number 3 (2017), pp. 323-335 International Research Publication House http://www.irphouse.com Edge-Odd Graceful Labeling
More informationSunoj B S *, Mathew Varkey T K Department of Mathematics, Government Polytechnic College, Attingal, Kerala, India
International Journal of Scientific Research in Computer Science, Engineering and Information Technology 2018 IJSRCSEIT Volume 3 Issue 1 ISSN : 256-3307 Mean Sum Square Prime Labeling of Some Snake Graphs
More informationVertex-Mean Graphs. A.Lourdusamy. (St.Xavier s College (Autonomous), Palayamkottai, India) M.Seenivasan
International J.Math. Combin. Vol. (0), -0 Vertex-Mean Graphs A.Lourdusamy (St.Xavier s College (Autonomous), Palayamkottai, India) M.Seenivasan (Sri Paramakalyani College, Alwarkurichi-67, India) E-mail:
More informationOn Sequential Topogenic Graphs
Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 36, 1799-1805 On Sequential Topogenic Graphs Bindhu K. Thomas, K. A. Germina and Jisha Elizabath Joy Research Center & PG Department of Mathematics Mary
More informationCordial Double-Staircase Graphs
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 7 (2017), pp. 3395-3401 Research India Publications http://www.ripublication.com Cordial Double-Staircase Graphs K. Ameenal
More informationInternational Journal of Mathematical Archive-6(8), 2015, Available online through ISSN
International Journal of Mathematical Archive-6(8), 2015, 66-80 Available online through www.ijma.info ISSN 2229 5046 SUBDIVISION OF SUPER GEOMETRIC MEAN LABELING FOR TRIANGULAR SNAKE GRAPHS 1 S. S. SANDHYA,
More informationPROPERLY EVEN HARMONIOUS LABELINGS OF DISJOINT UNIONS WITH EVEN SEQUENTIAL GRAPHS
Volume Issue July 05 Discrete Applied Mathematics 80 (05) PROPERLY EVEN HARMONIOUS LABELINGS OF DISJOINT UNIONS WITH EVEN SEQUENTIAL GRAPHS AUTHORS INFO Joseph A. Gallian*, Danielle Stewart Department
More informationVertex-antimagic total labelings of graphs
Vertex-antimagic total labelings of graphs Martin Bača Department of Applied Mathematics Technical University, 0400 Košice, Slovak Republic e-mail: hollbaca@ccsun.tuke.sk François Bertault Department of
More informationSome Results on Super Heronian Mean. Labeling of Graphs
International Journal of Contemporary Mathematical Sciences Vol., 0, no. 0, - 9 HIKARI Ltd, www.m-hikari.com https://doi.org/0.9/ijcms.0. Some Results on Super Heronian Mean Labeling of Graphs S. S. Sandhya
More informationPrime Labeling For Some Octopus Related Graphs
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 12, Issue 6 Ver. III (Nov. - Dec.2016), PP 57-64 www.iosrjournals.org Prime Labeling For Some Octopus Related Graphs A.
More informationProperly even harmonious labelings of disconnected graphs
Available online at www.sciencedirect.com ScienceDirect AKCE International Journal of Graphs and Combinatorics 12 (2015) 193 203 www.elsevier.com/locate/akcej Properly even harmonious labelings of disconnected
More informationVertex Graceful Labeling of C j C k C l
Applied Mathematical Sciences, Vol. 8, 01, no. 8, 07-05 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.01.5331 Vertex Graceful Labeling of C j C k C l P. Selvaraju 1, P. Balaganesan,5, J. Renuka
More informationGovernment Arts College, Melur , Tamilnadu, India. pons
Volume 118 No. 10 018, 97-109 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.173/ijpam.v118i10.53 ijpam.eu ODD VERTEX MAGIC TOTAL LABELING OF SOME
More informationHypo-k-Totally Magic Cordial Labeling of Graphs
Proyecciones Journal of Mathematics Vol. 34, N o 4, pp. 351-359, December 015. Universidad Católica del Norte Antofagasta - Chile Hypo-k-Totally Magic Cordial Labeling of Graphs P. Jeyanthi Govindammal
More informationEdge Graceful Labeling of Some Trees
Global Journal of Mathematical Sciences: Theory and Practical. olume, Number (0), pp. - International Research Publication House http://www.irphouse.com Edge Graceful Labeling of Some Trees B. Gayathri
More information1. INTRODUCTION. In 1736, Leonhard Euler wrote a paper on the Seven Bridges of Königsberg
1. INTRODUCTION In 1736, Leonhard Euler wrote a paper on the Seven Bridges of Königsberg which is regarded as the first paper in the history of graph theory. Graph theory is now a major tool in mathematical
More informationEdge-Magic Labeling of some Graphs
International Journal of Fuzzy Mathematics and Systems. ISSN 2248-9940 Volume 2, Number 1 (2012), pp. 47-51 Research India Publications http://www.ripublication.com Edge-Magic Labeling of some Graphs A.
More informationOn the Graceful Cartesian Product of Alpha-Trees
Theory and Applications of Graphs Volume 4 Issue 1 Article 3 017 On the Graceful Cartesian Product of Alpha-Trees Christian Barrientos Clayton State University, chr_barrientos@yahoo.com Sarah Minion Clayton
More informationSome Graph Operations Of Even Vertex Odd Mean Labeling Graphs
Some Graph Operations Of Even Vertex Odd Mean Labeling Graphs M.Kannan, R.Virama Prasad and R.Gopi 3 Research Scholar,Research & Development Centre, Bharathiar University, Coimbatore 64 046, India. Department
More informationSome bistar related square sum graphs
(IJMTT) --Volume 47X Number July 2017 2017 Volume, Issue3 Y - Month Some bistar related square sum graphs G. V. Ghodasara 1, Mitesh J. Patel 2 1 Assistant Professor in Mathematics, H. & H. B. Kotak Institute
More informationGLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES GROUP S 3 CORDIAL PRIME LABELING OF WHEEL RELATED GRAPH B. Chandra *1 & R.
GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES GROUP S 3 CORDIAL PRIME LABELING OF WHEEL RELATED GRAPH B. Chandra *1 & R. Kala 2 *1 Reg. No. 7348, Research Scholar, Department of Mathematics, Manonmaniam
More informationResearch Article Harmonious Properties of Uniform k-distant Trees
Chinese Mathematics Volume 013, Article ID 75451, 4 pages http://dx.doi.org/10.1155/013/75451 Research Article Harmonious Properties of Uniform k-distant Trees M. Murugan School of Science, Tamil Nadu
More informationInternational Journal of Pure and Applied Mathematics
Volume 115 No. 9 017, 363-375 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu EVEN VERTEX MAGIC TOTAL LABELING C.T. NAGARAJ Research Scholar, Department
More informationVertex Magic Total Labelings of Complete Graphs 1
Vertex Magic Total Labelings of Complete Graphs 1 Krishnappa. H. K. and Kishore Kothapalli and V. Ch. Venkaiah Centre for Security, Theory, and Algorithmic Research International Institute of Information
More informationSuper Fibonacci Graceful Labeling Of Some Cycle Related Graphs
International Journal of Mathematics Trends and Technology (IJMTT) Volume 3 Number 3 - October06 Super Fibonacci Graceful Labeling Of Some Cycle Related Graphs D.Amuthavalli, M. Premkumar Assistant Professor
More informationCordial, Total Cordial, Edge Cordial, Total Edge Cordial Labeling of Some Box Type Fractal Graphs
International Journal of Algebra and Statistics Volume 1: 2(2012), 99 106 Published by Modern Science Publishers Available at: http://www.m-sciences.com Cordial, Total Cordial, Edge Cordial, Total Edge
More informationSUPER (a,d)-edge ANTIMAGIC TOTAL LABELING OF CONNECTED LAMPION GRAPH
SUPER (a,d)-edge ANTIMAGIC TOTAL LABELING OF CONNECTED LAMPION GRAPH Robiatul Adawiyah 13, Dafik 14, Slamin 15 Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there
More informationON DIFFERENCE CORDIAL GRAPHS
Mathematica Aeterna, Vol. 5, 05, no., 05-4 ON DIFFERENCE CORDIAL GRAPHS M. A. Seoud Department of Mathematics, Faculty of Science Ain Shams University, Cairo, Egypt m.a.seoud@hotmail.com Shakir M. Salman
More informationSmarandache Directionally n-signed Graphs A Survey
International J.Math. Combin. Vol.2(2013), 34-43 Smarandache Directionally n-signed Graphs A Survey P.Siva Kota Reddy (Department of Mathematics, Acharya Institute of Technology, Soladevanahalli, Bangalore-560
More informationStrong and Semi Strong Outer Mod Sum Graphs
Int. Journal of Math. Analysis, Vol. 7, 013, no., 73-83 Strong and Semi Strong Outer Mod Sum Graphs M. Jayalakshmi and B. Sooryanarayana Dept.of Mathematical and Computational Studies Dr.Ambedkar Institute
More informationGraceful Labelings for Sun Graph, Sun Extension Graph, Double Fan, and Leg Graph with Star
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 5 (017), pp. 1357-1364 Research India Publications http://www.ripublication.com Graceful Labelings for Sun Graph, Sun Extension
More informationRemainder Cordial Labeling of Graphs
Journal of Algorithms and Computation journal homepage: http://jac.ut.ac.ir Remainder Cordial Labeling of Graphs R. Ponraj 1, K. Annathurai and R. Kala 3 1 Department of Mathematics, Sri Paramakalyani
More informationChapter 5. E-cordial Labeling of Graphs
Chapter 5 E-cordial Labeling of Graphs 65 Chapter 5. E-cordial Labeling of Graphs 66 5. Introduction In 987 the concept of cordial labeling was introduced by Cahit [6] as a weaker version of graceful and
More informationResearch Article Tree-Antimagicness of Disconnected Graphs
Mathematical Problems in Engineering Volume 2015, Article ID 504251, 4 pages http://dx.doi.org/10.1155/2015/504251 Research Article Tree-Antimagicness of Disconnected Graphs Martin BaIa, 1 Zuzana Kimáková,
More informationSOME RESULTS ON EVEN VERTEX ODD MEAN LABELING GRAPHS
International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 2, February 2018, pp. 615 621 Article ID: IJMET_09_02_062 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=2
More informationOn super (a, d)-edge antimagic total labeling of disconnected graphs
On super (a, d)-edge antimagic total labeling of disconnected graphs I W. Sudarsana 1, D. Ismaimuza 1,E.T.Baskoro,H.Assiyatun 1 Department of Mathematics, Tadulako University Jalan Sukarno-Hatta Palu,
More informationInternational Research Journal of Engineering and Technology (IRJET) e-issn:
SOME NEW OUTCOMES ON PRIME LABELING 1 V. Ganesan & 2 Dr. K. Balamurugan 1 Assistant Professor of Mathematics, T.K. Government Arts College, Vriddhachalam, Tamilnadu 2 Associate Professor of Mathematics,
More informationVERTEX-MAGIC TOTAL LABELINGS OF DISCONNECTED GRAPHS
Journal of Prime Research in Mathematics Vol. (006), 147-156 VERTEX-MAGIC TOTAL LABELINGS OF DISCONNECTED GRAPHS SLAMIN 1,, A.C. PRIHANDOKO 1, T.B. SETIAWAN 1, F. ROSITA 1, B. SHALEH 1 Abstract. Let G
More informationMean, Odd Sequential and Triangular Sum Graphs
Circulation in Computer Science Vol.2, No.4, pp: (40-52), May 2017 https://doi.org/10.22632/ccs-2017-252-08 Mean, Odd Sequential and Triangular Sum Graphs M. A. Seoud Department of Mathematics, Faculty
More informationOn Strongly *-Graphs
Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences 54 (2): 179 195 (2017) Copyright Pakistan Academy of Sciences ISSN: 2518-4245 (print), 2518-4253 (online) Pakistan
More informationGraceful Labeling for Double Step Grid Graph
International Jornal of Mathematics And its Applications Volme 3, Isse 1 (015), 33 38. ISSN: 347-1557 International Jornal 347-1557 of Mathematics Applications And its ISSN: Gracefl Labeling for Doble
More informationHow to construct new super edge-magic graphs from some old ones
How to construct new super edge-magic graphs from some old ones E.T. Baskoro 1, I W. Sudarsana 2 and Y.M. Cholily 1 1 Department of Mathematics Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung
More informationarxiv: v1 [math.co] 28 Dec 2013
On Distance Antimagic Graphs arxiv:131.7405v1 [math.co] 8 Dec 013 Rinovia Simanjuntak and Kristiana Wijaya Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut
More informationEdge-Odd Graceful Labeling of Sum of K 2 & Null Graph with n Vertices and a Path of n Vertices Merging with n Copies of a Fan with 6 Vertices
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (2017), pp. 4943-4952 Research India Publications http://www.ripublication.com Edge-Odd Graceful Labeling of Sum of K
More informationCouncil for Innovative Research Peer Review Research Publishing System Journal: INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY
ABSTRACT Odd Graceful Labeling Of Tensor Product Of Some Graphs Usha Sharma, Rinku Chaudhary Depatment Of Mathematics and Statistics Banasthali University, Banasthali, Rajasthan-304022, India rinkuchaudhary85@gmail.com
More informationVertex Magic Total Labelings of Complete Graphs
AKCE J. Graphs. Combin., 6, No. 1 (2009), pp. 143-154 Vertex Magic Total Labelings of Complete Graphs H. K. Krishnappa, Kishore Kothapalli and V. Ch. Venkaiah Center for Security, Theory, and Algorithmic
More informationAlgorithm to Construct Super Vertex Magic Total Labeling of Complete Graphs
Algorithm to Construct Super Vertex Magic Total Labeling of Complete Graphs Krishnappa H K 1, N K Srinath 2 and S Manjunath 3 1 Assistant Professor, Dept. of CSE, RVCE., Bangalore, India. 2 Professor,
More information4 Remainder Cordial Labeling of Some Graphs
International J.Math. Combin. Vol.(08), 8-5 Remainder Cordial Labeling of Some Graphs R.Ponraj, K.Annathurai and R.Kala. Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-67, India. Department
More informationSome Results On Vertex Odd Divisor Cordial Labeling of Graphs
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 11 2017, 199 207 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Some Results
More informationTopological Integer Additive Set-Sequential Graphs. Received: 7 April 2015 / Accepted: 26 June 2015 / Published: 3 July 2015
Mathematics 2015, 3, 604-614; doi:10.3390/math3030604 OPEN ACCESS mathematics ISSN 2227-7390 www.mdpi.com/journal/mathematics Article Topological Integer Additive Set-Sequential Graphs Sudev Naduvath 1,
More informationVertex-graceful labelings for some double cycles
Vertex-graceful labelings for some double cycles Wai Chee SHIU Department of Mathematics Hong Kong Baptist University. June 28, 2011 Vertex-graceful labelings for some double cycles p. 1/2 Vertex-graceful
More informationCLASSES OF VERY STRONGLY PERFECT GRAPHS. Ganesh R. Gandal 1, R. Mary Jeya Jothi 2. 1 Department of Mathematics. Sathyabama University Chennai, INDIA
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 10 2017, 334 342 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Abstract: CLASSES
More informationCordial Labeling on Aztec Diamond Graphs Dr. K.Ameenal Bibi 1, T.Ranjani 2 1,2 P.G and Research Department of Mathematics,
International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) ISSN (rint): 2279-47 ISSN (Online): 2279-55 International
More informationChapter 4. square sum graphs. 4.1 Introduction
Chapter 4 square sum graphs In this Chapter we introduce a new type of labeling of graphs which is closely related to the Diophantine Equation x 2 + y 2 = n and report results of our preliminary investigations
More informationTIGHT LOWER BOUND FOR LOCATING-TOTAL DOMINATION NUMBER. VIT University Chennai, INDIA
International Journal of Pure and Applied Mathematics Volume 101 No. 5 2015, 661-668 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu PAijpam.eu TIGHT LOWER
More informationRadio Number for Special Family of Graphs with Diameter 2, 3 and 4
MATEMATIKA, 2015, Volume 31, Number 2, 121 126 c UTM Centre for Industrial and Applied Mathematics Radio Number for Special Family of Graphs with Diameter 2, 3 and 4 Murugan Muthali School of Science,
More informationSuper edge-magic total labeling of subdivided stars
Super edge-magic total labeling of subdivided stars K. Ali 1, M. Hussain 1, H. Shaker 1, M. Javaid, 1 Department of Mathematical Sciences, COMSATS Institute of Information Technology, Lahore, Pakistan
More informationSome Star Related Vertex Odd Divisor Cordial Labeling of Graphs
Annals o Pure and Applied Mathematics Vol. 6, No., 08, 385-39 ISSN: 79-087X (P), 79-0888(online) Published on 6 February 08 www.researchmathsci.org DOI: http://dx.doi.org/0.457/apam.v6na5 Annals o Some
More informationOn Balance Index Set of Double graphs and Derived graphs
International Journal of Mathematics and Soft Computing Vol.4, No. (014), 81-93. ISSN Print : 49-338 ISSN Online: 319-515 On Balance Index Set of Double graphs and Derived graphs Pradeep G. Bhat, Devadas
More information