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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 6 of 10

Explore more Topics under Discrete Mathematics

Q51.
A bridge can not be a part of _______

a.

a simple cycle

b.

a tree

c.

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

d.

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 _______

a.

subgraph

b.

tree

c.

hamiltonian cycle

d.

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 ______

a.

Complete bipartite graph

b.

Hamiltonian cycle

c.

Regular graph

d.

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.

a.

98

b.

13

c.

6

d.

34

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?

a.

11

b.

14

c.

18

d.

19

Discuss
Answer: (c).18
Q56.
______ is the maximum number of edges in an acyclic undirected graph with k vertices.

a.

k-1

b.

k²

c.

2k+3

d.

k³+4

Discuss
Answer: (a).k-1
Q57.
The minimum number of edges in a connected cyclic graph on n vertices is _____________

a.

n – 1

b.

n

c.

2n+3

d.

n+1

Discuss
Answer: (b).n
Q58.
The maximum number of edges in a 8-node undirected graph without self loops is ____________

a.

45

b.

61

c.

28

d.

17

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 _____

a.

n-1 and n+1

b.

v and k

c.

k+1 and v-k

d.

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 ___________

a.

n+2

b.

3ⁿ/²

c.

n²

d.

2ⁿ

Discuss
Answer: (b).3ⁿ/²
Page 6 of 10

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