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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 9 of 10

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Q81.
The chromatic number of a graph is the property of ____________

a.

graph coloring

b.

graph ordering

c.

group ordering

d.

group coloring

Discuss
Answer: (b).graph ordering
Q82.
If a graph G is k-colorable and k<n, for any integer n then it is ___________

a.

n-colorable

b.

n² nodes

c.

(k+n)-colorable

d.

(k³+n³+1) nodes

Discuss
Answer: (a).n-colorable
Q83.
If Cₙ is the nth cyclic graph, where n>3 and n is odd. Determine the value of X(Cₙ).

a.

32572

b.

16631

c.

3

d.

310

Discuss
Answer: (c).3
Q84.
Determine the density of a planar graph with 34 edges and 13 nodes.

a.

22/21

b.

12/23

c.

328

d.

576

Discuss
Answer: (a).22/21
Q85.
If the number of vertices of a chromatic polynomial PG is 56, what is the degree of PG?

a.

344

b.

73

c.

265

d.

56

Discuss
Answer: (d).56
Q86.
For a connected planar simple graph G=(V, E) with e=|E|=16 and v=|V|=9, then find the number of regions that are created when drawing a planar representation of the graph?

a.

321

b.

9

c.

1024

d.

596

Discuss
Answer: (b).9
Q87.
Suppose G be a connected planar graph of order n≥5 and size m. If the length of the smallest cycle in G is 5, then which of the following is true?

a.

(m+n)⁴>=mn

b.

m≤5/3(n−2)

c.

(m²+n)/3

d.

n>=(6/5)(n+1)

Discuss
Answer: (b).m≤5/3(n−2)
Q88.
What is the number of edges of the greatest planar subgraph of K₃,₂ where m,n≤3?

a.

18

b.

6

c.

128

d.

702

Discuss
Answer: (b).6
Q89.
A non-planar graph can have ____________

a.

complete graph

b.

subgraph

c.

line graph

d.

bar graph

Discuss
Answer: (b).subgraph
Q90.
A direct product of a group G possess which of the following characteristics?

a.

a multiplication of subgroups of G

b.

a factorization via subgroups of G

c.

a superset of subgroups of G

d.

a maximal power set of subgroups

Discuss
Answer: (b).a factorization via subgroups of G
Page 9 of 10

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