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.

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 6 of 10

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Q51.

A bridge can not be a part of _______

a simple cycle

a tree

a clique with size ≥ 3 whose every edge is a bridge

a graph which contains cycles

Discuss

Answer: (a).a simple cycle

Q52.

Any subset of edges that connects all the vertices and has minimum total weight, if all the edge weights of an undirected graph are positive is called _______

subgraph

tree

hamiltonian cycle

grid

Discuss

Answer: (b).tree

Q53.

G is a simple undirected graph and some vertices of G are of odd degree. Add a node n to G and make it adjacent to each odd degree vertex of G. The resultant graph is ______

Complete bipartite graph

Hamiltonian cycle

Regular graph

Euler graph

Discuss

Answer: (d).Euler graph

Q54.

Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50.

Discuss

Answer: (c).6

Q55.

What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?

Discuss

Answer: (c).18

Q56.

______ is the maximum number of edges in an acyclic undirected graph with k vertices.

k-1

k²

2k+3

k³+4

Discuss

Answer: (a).k-1

Q57.

The minimum number of edges in a connected cyclic graph on n vertices is _____________

n – 1

2n+3

n+1

Discuss

Answer: (b).n

Q58.

The maximum number of edges in a 8-node undirected graph without self loops is ____________

Discuss

Answer: (c).28

Q59.

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

n-1 and n+1

v and k

k+1 and v-k

k-1 and v-1

Discuss

Answer: (d).k-1 and v-1

Q60.

The 2ⁿ vertices of a graph G corresponds to all subsets of a set of size n, for n>=4. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements.
The number of connected components in G can be ___________

n+2

3ⁿ/²

n²

2ⁿ

Discuss

Answer: (b).3ⁿ/²

Page 6 of 10

Welcome to the Graphs and Graphs Properties MCQs Page

Graphs and Graphs Properties MCQs | Page 6 of 10

Explore more Topics under Discrete Mathematics

Logics and Proofs

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting Theory

Discrete Probability

Relations

Tree Properties

Boolean Algebra and Modeling Computations

Group Theory

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