Graph Theory MCQs | Graph Theory Short Questions and Answers

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Questions
41 An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are
A all of even degree
B all of odd degree
C of any degree
D even in number

Answer: all of even degree
42 The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
A Reflexive
B Transitive
C Symmetric
D None of these

Answer: Transitive
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43 In an undirected graph the number of nodes with odd degree must be
A Zero
B Odd
C Prime
D Even

Answer: Even
44 What is the probability of choosing correctly an unknown integer between 0 and 9 with 3 chances ?
A 963/1000
B 966/1000
C 968/1000
D None of these

Answer: 963/1000
45 The complete graph K, has... different spanning trees?
A nn-2
B n*n
C nn
D n2

Answer: nn-2
46 Eccentricity of a vertex denoted by e(v) is defined by.... ?
A max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v}
B min { d(u,v): u belongs to v, u does not equal to v }
C Both A and B
D None of these

Answer: max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v}
47 A graph G is called a ..... if it is a connected acyclic graph ?
A Cyclic graph
B Regular graph
C Tree
D Not a graph

Answer: Tree
48 Length of the walk of a graph is .... ?
A The number of vertices in walk W
B The number of edges in walk W
C Total number of edges in a graph
D Total number of vertices in a graph

Answer: The number of edges in walk W
49 If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called... ?
A K graph
B K-regular graph
C Empty graph
D All of above

Answer: K-regular graph
50 The number of colours required to properly colour the vertices of every planer graph is
A 2
B 3
C 4
D 5

Answer: 5
51 In how many ways can a president and vice president be chosen from a set of 30 candidates?
A 820
B 850
C 880
D 870

Answer: 870
52 Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three?
A 1/8
B 1
C 7
D 3

Answer: 7
53 In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities?
A 100
B 120
C 110
D 150

Answer: 120
54 The number of colours required to properly color vertices of every planar graph is
A 2
B 3
C 4
D 5

Answer: 2

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