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Welcome to the Graphs and Graphs Properties MCQs Page

Dive deep into the fascinating world of Graphs and Graphs Properties with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Graphs and Graphs Properties, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Graphs and Graphs Properties, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Graphs and Graphs Properties. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Graphs and Graphs Properties. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Graphs and Graphs Properties MCQs | Page 7 of 10

Explore more Topics under Discrete Mathematics

Q61.
A graph which has the same number of edges as its complement must have number of vertices congruent to ______ or _______ modulo 4(for integral values of number of edges).

a.

6k, 6k-1

b.

4k, 4k+1

c.

k, k+2

d.

2k+1, k

Discuss
Answer: (c).k, k+2
Q62.
Every Isomorphic graph must have ________ representation.

a.

cyclic

b.

adjacency list

c.

tree

d.

adjacency matrix

Discuss
Answer: (d).adjacency matrix
Q63.
A cycle on n vertices is isomorphic to its complement. What is the value of n?

a.

5

b.

32

c.

17

d.

8

Discuss
Answer: (a).5
Q64.
How many perfect matchings are there in a complete graph of 10 vertices?

a.

60

b.

945

c.

756

d.

127

Discuss
Answer: (b).945
Q65.
A graph G has the degree of each vertex is ≥ 3 say, deg(V) ≥ 3 ∀ V ∈ G such that 3|V| ≤ 2|E| and 3|R| ≤ 2|E|, then the graph is said to be ________ (R denotes region in the graph)

a.

Planner graph

b.

Polyhedral graph

c.

Homomorphic graph

d.

Isomorphic graph

Discuss
Answer: (b).Polyhedral graph
Q66.
A complete n-node graph Kn is planar if and only if _____________

a.

n ≥ 6

b.

n² = n + 1

c.

n ≤ 4

d.

n + 3

Discuss
Answer: (c).n ≤ 4
Q67.
A graph is ______ if and only if it does not contain a subgraph homeomorphic to k₅ or k₃,₃.

a.

bipartite graph

b.

planar graph

c.

line graph

d.

euler subgraph

Discuss
Answer: (b).planar graph
Q68.
An isomorphism of graphs G and H is a bijection f the vertex sets of G and H. Such that any two vertices u and v of G are adjacent in G if and only if ____________

a.

f(u) and f(v) are contained in G but not contained in H

b.

f(u) and f(v) are adjacent in H

c.

f(u * v) = f(u) + f(v)

d.

f(u) = f(u)² + f(v)²

Discuss
Answer: (b).f(u) and f(v) are adjacent in H
Q69.
What is the grade of a planar graph consisting of 8 vertices and 15 edges?

a.

30

b.

15

c.

45

d.

106

Discuss
Answer: (a).30
Q70.
A _______ is a graph with no homomorphism to any proper subgraph.

a.

poset

b.

core

c.

walk

d.

trail

Discuss
Answer: (b).core
Page 7 of 10

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