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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 5 of 10

Explore more Topics under Discrete Mathematics

Q41.
In a 7-node directed cyclic graph, the number of Hamiltonian cycle is to be ______

a.

728

b.

450

c.

360

d.

260

Discuss
Answer: (c).360
Q42.
If each and every vertex in G has degree at most 23 then G can have a vertex colouring of __________

a.

24

b.

23

c.

176

d.

54

Discuss
Answer: (a).24
Q43.
Triangle free graphs have the property of clique number is __________

a.

less than 2

b.

equal to 2

c.

greater than 3

d.

more than 10

Discuss
Answer: (d).more than 10
Q44.
Berge graph is similar to ______ due to strong perfect graph theorem.

a.

line graph

b.

perfect graph

c.

bar graph

d.

triangle free graph

Discuss
Answer: (b).perfect graph
Q45.
Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?

a.

4

b.

0

c.

2

d.

5

Discuss
Answer: (c).2
Q46.
A ______ is a graph which has the same number of edges as its complement must have number of vertices congruent to 4m or 4m modulo 4(for integral values of number of edges).

a.

Subgraph

b.

Hamiltonian graph

c.

Euler graph

d.

Self complementary graph

Discuss
Answer: (d).Self complementary graph
Q47.
In a ______ the vertex set and the edge set are finite sets.

a.

finite graph

b.

bipartite graph

c.

infinite graph

d.

connected graph

Discuss
Answer: (b).bipartite graph
Q48.
If G is the forest with 54 vertices and 17 connected components, G has _______ total number of edges.

a.

38

b.

37

c.

17/54

d.

17/53

Discuss
Answer: (b).37
Q49.
The number of edges in a regular graph of degree 46 and 8 vertices is ____________

a.

347

b.

230

c.

184

d.

186

Discuss
Answer: (c).184
Q50.
An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G?

a.

1/2¹⁰¹

b.

1/50

c.

1/100

d.

1/20

Discuss
Answer: (b).1/50
Page 5 of 10

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