DS UNIT 4. Matoshri College of Engineering and Research Center Nasik Department of Computer Engineering Discrete Structutre UNIT - IV

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1 Sr.No. Question Option A Option B Option C Option D Class : S.E.Comp Which one of the following is the example of non linear data structure Let A be an adjacency matrix of a graph G. The ij th entry in the matrix AK, gives For an undirected graph with n vertices and e edges, the sum of the degree of each vertex is equal to An undirected graph G with n vertices and e edges is represented by adjacency list. What is the time required to generate all the connected components? The maximum degree of any vertex in a simple graph with n vertices is The data structure required for Breadth First Traversal on a graph is Matoshri College of Engineering and Research Center Nasik Department of Computer Engineering Discrete Structutre UNIT - IV Subject : Discrete Structutre Correct Option Graph Binary Tree Queue Link List A 1 The number of paths of length K from vertex Vi to vertex Vj. Shortest path of K edges from vertex Vi to vertex Vj. Length of a Eulerian path from vertex Vi to vertex Vj. Length of a Hamiltonian cycle from vertex Vi to vertex Vj. Marks B 2 2n (2n-1)/2 2e e2/2 C 2 O (n) O (e) O (e+n) O (e2 ) C 2 n 1 n+1 2n 1 n A 2 queue (LIFO) stack (FIFO) array tree A 2 7 A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are greater than n 1 less than n(n 1) greater than n(n 1)/2 less than n2/2 A 2 8 An adjacency matrix representation of a graph cannot contain information of : 9 A queue is a, In Breadth First Search of Graph, which of the following data structure is used? For an undirected graph G with n vertices and e edges, the sum of the degrees of each vertex is Indicate which, if any, of the following five graphs G = (V,E, ), V = 5, is n isomorphic to any of the other four. t nodes edges direction of edges parallel edges D 2 FIFO (First In First Out) list. LIFO (Last In First Out) list. Ordered array. Linear tree. A 2 Stack. Queue. Linked List. None of the above. B 2 ne 2n 2e en C 2 A {1,3}B {2,4} C{1,2}D{2,3} E{3,5}F {4,5} {1,2}b {1,2}c {2,3}d {3,4}e {3,4}a {4,5} b {4,5}f {1,3} e {1,3} d {2,3}c {2,4}a {4,5} 1 {1,}2 {2,3}3 {2,3} 4{3,4} 5{4,5}6 {4,5} A 4 Page 1

2 A graph with V = {1, 2, 3, 4} is described by = a {1,2} b {1,2} c {1,4} d {2,3} e {3,4} f {3,4}How many Hamiltonian cycles does it have? A graph with V = {1, 2, 3, 4} is described by = a {1,2} b {1,2} c {1,4} d {2,3} e {3,4} f {3,4} It has weights on its edges given by = a b c d e f How many minimum spanning trees does it have? For which of the following does there exist a graph G = (V,E, ) satisfying the specified conditions? For which of the following does there exist a simple graph G = (V,E) satisfying the specified conditions? C B 4 A tree with 9 vertices and the sum of the degrees of all the vertices is 18. It has 3 components 20 vertices and 16 A graph with 5 components 12 vertices and 7 It has 6 vertices, 11 edges, and more than one component. A graph with 5 components 30 vertices and 24 It is connected and has 10 edges 5 vertices and fewer than 6 cycles. A graph with 9 vertices, 9 edges, and no cycles. It has 7 vertices, 10 edges, and more than two components. B 4 D 4 17 The number of simple digraphs with V = 3 is A 4 18 The number of simple digraphs with V = 3 and exactly 3 edges is D 4 19 The number of oriented simple graphs with V = 3 is D 4 20 The number of oriented simple graphs with V = 4 and 2 edges is C 4 21 Compute the total number of bicomponents in all of the following three simple graphs, G = (V,E) with V = 5. For each graph the edge sets are as follows: E = {1, 2}, {2, 3}, {3, 4}, {4, 5}, {1, 3}, {1, 5}, {3, 5} E = {1, 2}, {2, 3}, {3, 4}, {4, 5}, {1, 3} C 4 22 E = {1, 2}, {2, 3}, {4, 5}, {1, 3} a {1,2} b {2,3} c b{4,5} a {1,3} e b {4,5} f {1,3} e a {1,2} b {2,3} Indicate which, if any, of the following five graphs G = (V,E, {1,2} d {1,3} e {1,3} d {2,3} c {1,3} d {2,3} c c {1,2} d {2,3} e ), V = 5, isot connected. {2,3} f {4,5}. {2,5} f {4,5}. {2,4} a {4,5}. {3,4} f {1,5}. A 4 23 Indicate which, if any, of the following five graphs G = (V,E, ), V = 5, have an Eulerian circuit. F{1,2} B {1,2} C {2,3} D{3,4} E {4,5} A {4,5}. b {4,5} f {1,3} e {1,3} d {2,3} c {2,4} a {4,5}. 1 {1,2} 2 {1,2} 3 {2,3} 4 {3,4}5 {4,5} 6 {4,5}. a {1,3} b {3,4} c{1,2} d {2,3} e {3,5} f {4,5}. D 4 Page 2

3 24 A graph is a set of integers; a set of integers; 25 The degree of a vertex in a graph is 26 A graph is defined in part by vertices in its graph; exactly one ordered pair of other vertices incident to it a relation; a set of vertices and a set of edges; paths; a cycle; a set of edges; C 1 distinct connected subgraphs; one path joining each pair of B 1 C 2 27 series of edges that connect two vertices is called a path; a cycle; a connection; a tree; A 1 To design a communications network that joins all nodes minimal spanning 28 path; expression tree; search tree B 2 without excessive lines, we must find a three; 29 A series of edges that form a path from a vertex to itself is a spanning path; a cycle; a connection; a tree; B 1 30 A weighted graph has an adjacency matrix that is integers; 31 In a connected graph an edge exists between each pair of vertices. 32 A graph may be fully represented by its its edges; 33 The prerequesite relationships among required courses in the Computer Science major form a real numbers and.; booleans; A 2 T F A 1 binary tree; 34 Graph path search involves finding a set of 35 Two graphs are isomorphic iff they have the same numbers of vertices and edges; linked list; sequence of they have the same degrees; an adjacency matrix; directed acyclic graph; set of edges; bijections of a special kind exist between their sets of vertices and edges; the degrees of its C 2 weighted graph; C 2 minimal set of edges; they have no vertices in common; B 2 C 2 36 Graphs for which bijections of a special kind exist between their sets of vertices and edges are nested; transitive; undecidable; isomorphic D 2 37 Graphs that have the same structure are nested; transitive; undecidable; isomorphic C 2 38 Graph isomorphism invariant properties include having the same numbers of vertices and satisfiability; reachability; well ordering; A 2 39 The reflexive transitive closure of maps from states to states; states and symbols to states; states and strings to states; states and symbols to symbols; none of these 2 Page 3

4 40 How many edges are there in an undirected graph with two vertices of degree 7, four vertices of degree 5, and the remaining four vertices of degree is 6? A 4 41 A graph in which all nodes are of equal degrees is known as: Multigraph Complete lattice Regular graph non regular graph B Suppose v is an isolated vertex in a graph, then the degree of v is: In an undirected graph nodes with odd degree must be 44 Which of the following statement is true: A 2 Zero Odd Prime Even D 2 Every graph is not its own subgraph The terminal vertex of a graph are of degree two. A tree with n vertices has n A single vertex in graph G is a subgraph of G. D 2 45 The length of Hamiltonian Path in a connected graph of n vertices is n 1 n n+1 n/2 A 2 46 A graph with one vertex and no edges is: multigraph digraph isolated graph trivial graph D 2 47 A complete graph of n vertices should have n-1 n n(n-1)/2 n(n+1)/2 C 2 48 A Euler graph is one in which Only two vertices are of odd degree and rests are even Only two vertices are of even degree and rests are odd All the vertices are of odd degree All the vertices are of even degree D 2 49 A spanning tree of a graph is one that includes All the vertices of the graph All the edges of the graph Only the vertices of odd degree Only the vertices of even degree A 2 50 In multigraph In Pseudographs Simple graph more than one edge can join two vertices, but no edge can join to itself. more than one edge can join two vertices, but no edge can join to itself. self loops as well as parallel edges are allowed. parallel edges allowed but not selfloops self loops as well as parallel edges are allowed. no self loop and no parallel edges are present. A or B None of these C 1 A & B None of these B 1 A & B None of these B 1 Page 4

5 53 A simple graph with n vertices is known as complete graph if degree of each vertex is n (n-1) (n-1)/n None of these B 1 54 A Vertex with degree 1 is known as Isolated vertex root pendent vertex None of these C 1 55 In handshaking lemma the sum of the degrees of the vertices of a graph is edges Twice Thrice Equal None of these A 1 56 How many nodes are necessary to construct 8 edges in which each node is of degree B 2 57 If in a graph each edge has a direction, the graph known as directed graph simple graph weighted graph None of these A 2 58 In a graph if degree of each vertex is same then the graph is known as directed graph simple graph weighted graph Regular graph D 1 59 G is a graph whose set of vertices is v. If V can be V1 V2 & V1 partitioned into two subsets V1 & V2 such that every edge V1 V2 V1 V2 V2 of G joins V1 with V2 also None of these C 2 60 A graph with n vertices and no edge is known as null graph bipartite graph simple graph None of these A 1 61 How many edges has of the K 6 graphs How many edges has of the K 4,6 graph C 2 63 A graph G is called if the edges do not repeat in the path. Simple path A & B None of these B 1 64 A closed path is known as Simple path A & B None of these A 1 65 A graph is said to be elementry circuit if it does not include the same vertex twice except the end vertex. elementry circuit simple graph None of these B 1 66 A path is known as if every edge of the graph appers Hamiltonoin exactly once in the path. Hamiltonoin path Eulerian Eulerian path D 1 67 The circuit which contains every edge of the graph exactly Hamiltonoin once is called Hamiltonoin path Eulerian Eulerian path C 1 68 A path in a connected graph G is a if it Hamiltonoin contains every vertex of G exactly once. Hamiltonoin path Eulerian Eulerian path B 1 69 A circuit in a connected graph G is a if it Hamiltonoin contains every vertex of G exactly once except the first and the last vertex Hamiltonoin path Eulerian Eulerian path A 1 A graph is said to be if it can be drawn on 70 a plane in such a way that no edge cross one another, except at common vertices. Planer Graph simple Graph Regular graph None of these A 1 Page 5

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