Top MCQs on Graph Theory in Mathematics

Question 31

Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between

• k and n
• k - 1 and k + 1
• k - 1 and n - 1
• k + 1 and n - k

Question 32

How many perfect matchings are there in a complete graph of 6 vertices ?

• 15
• 24
• 30
• 60

Question 33

A graph G = (V, E) satisfies |E| ≤ 3 |V| - 6. The min-degree of G is defined as . Therefore, min-degree of G cannot be

• 3
• 4
• 5
• 6

Question 34

The minimum number of colours required to colour the vertices of a cycle with η nodes in such a way that no two adjacent nodes have the same colour is

• 2
• 3
• 4
• n - 2⌊n/2⌋ + 2

Question 35

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 36

Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is _______________.

• 24
• 20
• 32
• 64

Question 37

A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on n vertices, n is

• A multiple of 4
• Even
• Odd
• Congruent to 0 mod 4, or 1 mod 4

Question 38

In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is True?

• A tree has no bridge
• A bridge cannot be part of a simple cycle
• Every edge of a clique with size ≥ 3 is a bridge (A clique is any complete subgraph of a graph)
• A graph with bridges cannot have a cycle

Question 39

What is the number of vertices in an undirected connected graph with 27 edges, 6 vertices of degree 2, 3 vertices of degree 4 and remaining of degree 3?

• 10
• 11
• 18
• 19

Question 40

The minimum number of colours that is sufficient to vertex-colour any planar graph is _______________ [This Question was originally a Fill-in-the-blanks Question]

• 1
• 2
• 3
• 4