Data Struct. & Prob. Solving, M.C.Q. BANK, FOR UNIT 3, SECOND YEAR COMP. ENGG. SEM 1, 2012 PATTERN, U.O.P.

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1 UNIT distribution for = 11 (Only 1 will be asked for marks, s will be asked for 1 & s asked for marks ) Syllabus for Graphs Programmers perspective of graphs, Graph operations, storage structure, Traversal: readth first, depth first graph algorithms, Graph as an T, pplications of graph: GIS based, nalysis of algorithms, spanning Trees, onnected omponents Reference ook. E. Horowitz S. Sahani,. Mehata, Fundamentals of data structures in ++, Galgotia ook Source, New elhi, 1995, ISN: R. Gilberg,. Forouzan, ata Structures: pseudo code approach with ++, engage Learning Practical ssignment ased on 1. news paper delivery boy every day drops news paper in a society having many lanes & each lane have many houses. esign a program to provide different paths that he could follow & also suggest the path which will make him to finish his task with less effort. Solve the problem by suggesting appropriate data structures. esign necessary class.. Write a program to find shortest path for given source & destination of a given graph using.. Write a Java program to implement topological sorting on graph using object oriented programming features esign necessary class. M..Q. ank for The number of circuit in a tree with n nodes is zero 1 n/ nswer 1 10 graph is a tree if and only if it Is completely connected EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..1

2 Is minimaly connected ontains a circuit Is planar nswer 11 The minimum number of spanning tree in a connected graph with n node is 1 n/ nswer 1 The rank of a graph with n vertices's, edges and k components is n e n+k n+k nswer c 1 The nullity of a graph with n vertices's,e edge and k components is n e n+k n k n+k nswer EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..

3 15 What is the edge connectivity of a complete graph with n vertices's? 1 n+1 n(n+1)/ nswer 16 Let a graph G has edge connectivity and node connectivity then α< β α= β α>=β α<=β nswer 19 graph with n vertices's and edge that is not a tree,is connected disconnected eular circuit nswer 1 graph consisting of only isolated n vertices's is 1 chromatic chromatic chromatic EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..

4 n chromatic nswer 15 graph with one or more edge (without self loop) is at least 1 chromatic chromatic chromatic n chromatic nswer 16 complete graph with n vertices's is chromatic n/ chromatic ()chromatic n chromatic nswer 1 n undirected graph with n vertices's and e edges are represented by adjacency matrix. What is the time required to determine whether the graph is connected? O(e) O(n) O(n ) O(e+n) nswer orrect Option () EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..

5 n undirected graph with n vertices's and e edges are represented by adjacency matrix. What is the time required to determine the degree of any vertex O(e) O(n) O(e+n) O (n ) nswer orrect Option () The minimum number of edges in a connected cyclic graph on n vertices's is n n+1 None of these nswer The minimum number of colors needed to color a graph having n (>) vertices and edges is 1 nswer The max.degree of any vertex in simple graph with n vartices is N N+1 EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..5

6 nswer orrect option Which of the following is useful in traversing a given graph by breadth first search? stacks set lists Queue nswer The nu. of edges in a regular graph of degree d and vertices's n is Max.of n,d n+d nd nd/ nswer orrect option The maximum degree of any vertex in a simple graph with n vertices's is n n+1 nswer EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..6

7 The number of edges in a regular graph of degree d and n vertices's is maximum of n, d n+d nd nd/ nswer The correct matching for the following pairs is () ll pairs shortest path () Quick sort () Minimum weight spanning tree () onnected omponents (1) Greedy () epth first search () ynamic programming () ivide and conquer,, 1,,, 1,,,, 1, 1,, nswer The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences cannot be the degree sequence of any graph? I. 7, 6, 5,,,,, 1 II. 6,6,6,6,,,, III. 7,6,6,,,,, IV. 8, 7, 7, 6,,, 1, 1 I and II III and IV IV only II and IV only nswer EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..7

8 What is the number of nodes in the largest maximal independent set of the complete bipartite graph K (, )? 6 nswer directed graph with n vertices & e edges are represented by adjacency matrix. What is the time required to determine the in degree of vertex? O(e) O(n) O(n) O(e+n) nswer orrect Option () n undirected graph G with n vertices & e edges are represented by adjacency list. What is the time required to determine the total number of edges in G? O(e) O(n) O(n) O(e+n) nswer orrect Option() EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..8

9 onsider an undirected graph G with n vertices & e edges. What is the time taken by depth first search (FS) if the graph is represented by I. adjacency matrix, & (ii) adjacency list O(n), O(n) O(n), O(e) O(e), O(n) O(e+n), O(e) nswer orrect option () n undirected graph G with n vertices & e edges is represented by adjacency list. What is the time required to generate all the connected components? O(n) O(e) O(e+n) O(e) nswer orrect Option () Which of the following statements is false? Every tree is a bipartite graph tree contains a cycle tree with n nodes contains edges tree is a connected graph nswer orrect Option() graph G with n nodes is bipartite if it contains N edges cycle of odd length EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..9

10 No cycle of odd length n^ edges nswer orrect Option() Keep It lank The time required to find shortest path in a graph with n vertices's & e edges is O(e) O(n) O(e) O(n) nswer orrect Option () What is true for the complete bipartite graphs k(,) and k(,)? oth are planer Neither is planer oth are isomorphic None of the above nswer 1 onsider the graph shown in figure 1 which are the following is a valid strong component? EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..10

11 ,,,,,,,, nswer onsider the graph shown in figure below which of the following is a valid topological sorting? nswer What is the shortest distance for a path from to K? EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..11

12 nswer What is the weight of the minimal spanning tree for the graph shown below nswer EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..1

13 onsider the graph shown below What should be the labels of nodes marked 1 and if the breadth first traversal yields the list E? and E E and Unpredictable None of the above nswer onsider the undirected weighted graph shown in figure below The minimum cost spanning tree has the cost? EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..1

14 18 0 nswer The max.degree of any vertex in simple graph with n vartices is N N+1 nswer orrect option The nu. of edges in a regular graph of degree d and vertices's n is Max.of n,d n+d nd nd/ nswer orrect option Which of the following is useful in a traversing a given graph by breadth first search Stack Set List Queue nswer orrect option EPRTMENT OF OMPUTER ENGINEERING, MTOSHRI OLLEGE OF ENGINEERING & R.. NSHIK, PGE NO..1