Graph Theory Objective type Questions and Answers

(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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