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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 2 of 10

Explore more Topics under Discrete Mathematics

Q11.
An undirected graph has 8 vertices labelled 1, 2, …,8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8?

a.

15

b.

8

c.

5

d.

23

Discuss
Answer: (b).8
Q12.
G is an undirected graph with n vertices and 26 edges such that each vertex of G has a degree at least 4. Then the maximum possible value of n is ___________

a.

7

b.

43

c.

13

d.

10

Discuss
Answer: (c).13
Q13.
Hasse diagrams are first made by ______

a.

A.R. Hasse

b.

Helmut Hasse

c.

Dennis Hasse

d.

T.P. Hasse

Discuss
Answer: (b).Helmut Hasse
Q14.
If a partial order is drawn as a Hasse diagram in which no two edges cross, its covering graph is called ______

a.

upward planar

b.

downward planar

c.

lattice

d.

biconnected components

Discuss
Answer: (a).upward planar
Q15.
If the partial order of a set has at most one minimal element, then to test whether it has a non-crossing Hasse diagram its time complexity __________

a.

NP-complete

b.

O(n²)

c.

O(n+2)

d.

O(n³)

Discuss
Answer: (a).NP-complete
Q16.
Which of the following relation is a partial order as well as an equivalence relation?

a.

equal to(=)

b.

less than(<)

c.

greater than(>)

d.

not equal to(!=)

Discuss
Answer: (a).equal to(=)
Q17.
The relation ≤ is a partial order if it is ___________

a.

reflexive, antisymmetric and transitive

b.

reflexive, symmetric

c.

asymmetric, transitive

d.

irreflexive and transitive

Discuss
Answer: (a).reflexive, antisymmetric and transitive
Q18.
In which of the following relations every pair of elements is comparable?

a.

≤

b.

!=

c.

>=

d.

==

Discuss
Answer: (a).≤
Q19.
In a poset (S, ⪯), if there is no element n∈S with m<n, then which of the following is true?

a.

an element n exists for which m=n

b.

An element m is maximal in the poset

c.

A set with the same subset of the poset

d.

An element m is minimal in the poset

Discuss
Answer: (b).An element m is maximal in the poset
Q20.
In a poset P({v, x, y, z}, ⊆) which of the following is the greatest element?

a.

{v, x, y, z}

b.

1

c.

∅

d.

{vx, xy, yz}

Discuss
Answer: (a).{v, x, y, z}
Page 2 of 10

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