Top MCQs on Graph Theory in Mathematics

Question 71

A graph in which all nodes are of equal degree, is known as

• Multigraph
• Non regular graph
• Regular graph
• Complete graph

Question 72

In a graph G there is one and only one path between every pair of vertices then G is a

• Path
• Walk
• Tree
• Circuit

Question 73

A simple graph ( a graph without parallel edge or loops) with n vertices and k components can have at most

• n edges
• n-k edges
• (n − k)(n − k + 1) edges
• (n − k)(n − k + 1)/2 edges

Question 74

If G is a graph with e edges and n vertices, the sum of the degrees of all vertices in G is

• e
• e/2
• e²
• 2 e

Question 75

The number of distinct simple graphs with up to three nodes is

• 15
• 10
• 7
• 9

Question 76

The maximum number of edges in a n-node undirected graph without self loops is

• n²
• n * (n-1)/2
• n - 1
• (n + 1) * n/2

Question 77

Consider the graph shown in the figure below: Which of the following is a valid strong component?

• a, c, d
• a, b, d
• b, c, d
• a, b, c

Question 78

A graph with n vertices and n-1 edges that is not a tree, is

• Connected
• Disconnected
• Euler
• A circuit

Question 79

If a graph requires k different colours for its proper colouring, then the chromatic number of the graph is

• 1
• k
• k-1
• k/2

Question 80

Let X be the adjacency matrix of a graph G with no self loops. The entries along the principal diagonal of X are

• all zeros
• all ones
• both zeros and ones
• different