Top MCQs on Graph Theory in Mathematics

Question 61

How many diagonals can be drawn by joining the angular points of an octagon?

• 14
• 20
• 21
• 28

Question 62

The number of edges in a \'n\' vertex complete graph is ?

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

Question 63

Which of the following statement(s) is/are false ? (a) A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree. (b) A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree. (c) A complete graph (K_n) has a Hamilton Circuit whenever n ≥ 3. (d)A cycle over six vertices (C₆) is not a bipartite graph but a complete graph over 3 vertices is bipartite. Codes:

• (a) only
• (b) and (c)
• (c) only
• (d) only

Question 64

Consider the graph given below: The two distinct sets of vertices, which make the graph bipartite are:

• (v1, v4, v6); (v2, v3, v5, v7, v8)
• (v1, v7, v8); (v2, v3, v5, v6)
• (v1, v4, v6, v7); (v2, v3, v5, v8)
• (v1, v4, v6, v7, v8); (v2, v3, v5)

Question 65

A tree with n vertices is called graceful, if its vertices can be labelled with integers 1, 2,....n such that the absolute value of the difference of the labels of adjacent vertices are all different. Which of the following trees are graceful? codes:

• (a) and (b)
• (b) and (c)
• (a) and (c)
• (a), (b) and (c)

Question 66

Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ? (a) deg (v) ≥ n / 2 for each vertex of G (b) |E(G)| ≥ 1 / 2 (n - 1) (n - 2) + 2 edges (c) deg (v) + deg (w) ≥ n for every n and v not connected by an edge.

• (a) and (b)
• (b) and (c)
• (a) and (c)
• (a), (b) and (c)

Question 67

Consider the given graph Its Minimum Cost Spanning Tree is __________. (1) (2) (3) (4)

• (1)
• (2)
• (3)
• (4)

Question 68

If node A has three siblings and B is parent of A, what is the degree of A?

• 0
• 3
• 4
• None of the above

Question 69

How many edges are there in a forest with v vertices and k components?

• (v + 1) − k
• (v + 1)/2 − k
• v − k
• v + k

Question 70

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 down between

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