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Welcome to the Tree Properties MCQs Page

Dive deep into the fascinating world of Tree Properties with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Tree Properties, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Tree 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 Tree 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 Tree Properties. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Tree Properties MCQs | Page 2 of 6

Explore more Topics under Discrete Mathematics

Q11.
If two cycle graphs Gm and Gn are joined together with a vertex, the number of spanning trees in the new graph is ______

a.

m+n-1

b.

m-n

c.

m*n

d.

m*n+1

Discuss
Answer: (c).m*n
Q12.
For an n-vertex undirected graph, the time required to find a cycle is ____________

a.

O(n)

b.

O(n²)

c.

O(n+1)

d.

O(logn)

Discuss
Answer: (a).O(n)
Q13.
A binary cycle space forms a ______ over the two element field.

a.

triangular graph

b.

vector space

c.

binary tree

d.

hamiltonian graph

Discuss
Answer: (b).vector space
Q14.
If G is a simple graph with n-vertices and n>=3, the condition for G has a Hamiltonian circuit is __________

a.

the degree of each vertex is at most n/2

b.

the degree of each vertex is equal to n

c.

the degree of every vertex is at least n+1/2

d.

the degree of every vertex in G is at least n/2

Discuss
Answer: (d).the degree of every vertex in G is at least n/2
Q15.
What is a separable graph?

a.

A disconnected graph by deleting a vertex

b.

A disconnected graph by removing an edge

c.

A disconnected graph by removing one edge and a vertex

d.

A simple graph which does not contain a cycle

Discuss
Answer: (a).A disconnected graph by deleting a vertex
Q16.
How many edges are there in a complete graph of order 9?

a.

35

b.

36

c.

45

d.

19

Discuss
Answer: (b).36
Q17.
How many cycles are there in a wheel graph of order 5?

a.

6

b.

10

c.

25

d.

7

Discuss
Answer: (d).7
Q18.
The time complexity to find a Eulerian path in a graph of vertex V and edge E is _____________

a.

O(V²)

b.

O(V+E-1)

c.

O(V+E)

d.

O(E+1)

Discuss
Answer: (c).O(V+E)
Q19.
The time complexity to find shortest distances by using Dijkstra’s algorithm is __________

a.

O(E²)

b.

O(V+1-E)

c.

O(V+E)

d.

O(E+VlogV)

Discuss
Answer: (d).O(E+VlogV)
Q20.
Topological sorting of a graph represents _______ of a graph.

a.

linear probing

b.

linear ordering

c.

quadrilateral ordering

d.

insertion sorting

Discuss
Answer: (b).linear ordering
Page 2 of 6

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