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Graph Theory Quiz | Graph Theory Objective type Questions and Answers

Questions
21 How many onto (or surjective) functions are there from an n-element (n => 2) set to a 2-element set?
A 2n
B 2n - 1
C 2n - 2
D 2(2n – 2)

Answer: 2n - 2
22 Hasse diagram are drawn
A Partially ordered sets
B Lattices
C Boolean algebra
D None of these

Answer: Partially ordered sets
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23 In how many ways can 5 balls be chosen so that 2 are red and 3 are black
A 910
B 990
C 970
D None of these

Answer: 990
24 Circle has ____________
A No vertices
B Only 1 vertex
C 8 vertices
D None of these

Answer: No vertices
25 The proposition ~qvp is equivalent to
A p?q
B q?p
C p?q
D p?q

Answer: q?p
26 If B is a Boolean Algebra, then which of the following is true
A B is a finite but not complemented lattice
B B is a finite, complemented and distributive lattice
C B is a finite, distributive but not complemented lattice
D B is not distributive lattice

Answer: B is a finite, complemented and distributive lattice
27 If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is
A {(3,3), (3,4), (3,5)}
B {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}
C {(3,3), (3,5), (5,3), (5,5)}
D {(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}

Answer: {(3,3), (3,5), (5,3), (5,5)}
28 The number of distinguishable permutations of the letters in the word BANANA are,
A 60
B 36
C 20
D 10

Answer: 60
29 Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to
A 3
B 4
C 5
D 6

Answer: 6
30 A graph is tree if and only if
A Is planar
B Contains a circuit
C Is minimally
D Is completely connected

Answer: Is minimally
31 How many different words can be formed out of the letters of the word VARANASI?
A 64
B 120
C 40320
D 720

Answer: 720
32 Suppose v is an isolated vertex in a graph, then the degree of v is
A 0
B 1
C 2
D 3

Answer: 0
33 The complete graph with four vertices has k edges where k is
A 3
B 4
C 5
D 6

Answer: 6
34 Which one of the following statements is incorrect ?
A The number of regions corresponds to the cyclomatic complexity
B Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph
C Cyclometric complexity for a flow graph G is V(G) = E–N+2, where E is the number of edges & N is the number of nodes in the flow graph
D Cyclometric complexity for a flow graph G is V(G) = P + 1, where P is the number of predicate nodes contained in the flow graph G

Answer: Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph
35 Choose the most appropriate definition of plane graph
A A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices
B A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y
C A simple graph which is Isomorphic to Hamiltonian graph
D None of these

Answer: A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices
36 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
37 A graph with one vertex and no edges is
A multigraph
B digraph
C isolated graph
D trivial graph

Answer: trivial graph
38 In any undirected graph the sum of degrees of all the nodes
A Must be even
B Are twice the number of edges
C Must be odd
D Need not be even

Answer: Are twice the number of edges
39 In a graph if e=[u, v], Then u and v are called
A Endpoints of e
B Adjacent nodes
C Neighbors
D All of above

Answer: All of above
40 The number of leaf nodes in a complete binary tree of depth d is
A 2d
B 2d–1+1
C 2d+1+1
D 2d+1

Answer: 2d

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