Which of the following statements for a simple graph is correct?

a) Every path is a trail

b) Every trail is a path

c) Every trail is a path as well as every path is a trail

d) Path and trail have no relation

Option : a

Explanation: In a walk if the vertices are distinct it is called a path, whereas if the

edges are distinct it is called a trail.

In the given graph identify the cut vertices.

a) B and E

b) C and D

c) A and E

d) C and B

Option : d

For the given graph(G), which of the following statements is true?

a) G is a complete graph

b) G is not a connected graph

c) The vertex connectivity of the graph is 2

d) The edge connectivity of the graph is 1

Option : c

What is the number of edges present in a complete graph having n vertices?

a) (n*(n+1))/2

b) (n*(n-1))/2

c) n

d) Information given is insufficient

Option : b

The given Graph is regular.

a) True

b) False

Option : a

Explanation: In a regular graph, degrees of all the vertices are equal. In the given

graph the degree of every vertex is 3

In a simple graph, the number of edges is equal to twice the sum of the degrees of

the vertices.

a) True

b) False

Option : b

Explanation: The sum of the degrees of the vertices is equal to twice the number of

edges.

A connected planar graph having 6 vertices, 7edges contains

regions.

a) 15

b) 3

c) 1

d) 11

Option : b

Explanation: By euler’s formula the relation between vertices(n), edges(q) and

regions(r) is given by n-q+r=2.

What is the maximum number of edges in a bipartite graph having 10 vertices?

a) 24

b) 21

c) 25

d) 16

Option : c

Explanation: Let one set have n vertices another set would contain 10-n vertices.

Total number of edges would be n*(10-n), differentiating with respect to n, would

yield the answer.

Which of the following is true?

a) A graph may contain no edges and many vertices

b) A graph may contain many edges and novertices

c) A graph may contain no edges and no vertices

d) A graph may contain no vertices and many edges

Option : b

Explanation: A graph must contain at least one vertex.

For a given graph G having v vertices and e edges which is connected and has no

cycles, which of the following statements is true?

a) v=e

b) v = e+1

c) v + 1 = e

d) v = e-1

Option : b

Explanation: For any connected graph with no cycles the equation holds true

A graph with all vertices having equal degree is known as a

a) Multi Graph

b) Regular Graph

c) Simple Graph

d) Complete Graph

Option : b

Explanation: The given statement is the definition of regular graphs.