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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 5 of 6

Explore more Topics under Discrete Mathematics

Q41.
Spanning trees have a special class of depth-first search trees named _________

a.

Euclidean minimum spanning trees

b.

Tremaux trees

c.

Complete bipartite graphs

d.

Decision trees

Discuss
Answer: (b).Tremaux trees
Q42.
If the weight of an edge e of cycle C in a graph is larger than the individual weights of all other edges of C, then that edge ________

a.

belongs to an minimum spanning tree

b.

cannot belong to an minimum spanning tree

c.

belongs to all MSTs of the graph

d.

can not belong to the graph

Discuss
Answer: (b).cannot belong to an minimum spanning tree
Q43.
For every spanning tree with n vertices and n edges what is the least number of different Spanning trees can be formed?

a.

2

b.

5

c.

3

d.

4

Discuss
Answer: (c).3
Q44.
Time complexity of Prim’s algorithm is _________

a.

O((V+E)logV)

b.

O(E+V)

c.

O(E)

d.

O(V+1)

Discuss
Answer: (a).O((V+E)logV)
Q45.
What is the time complexity of Kruskal’s algorithm?

a.

O(ElogV)

b.

O(V+logE)

c.

O(E+1)

d.

O(V²)

Discuss
Answer: (a).O(ElogV)
Q46.
An immediate application of minimum spanning tree ______

a.

gesture analysis

b.

handwriting recognition

c.

fingerprint detection

d.

soft computing

Discuss
Answer: (b).handwriting recognition
Q47.
If minimum cost edge of a graph is unique, then that edge will be added to any MST. Choose the correct option.

a.

false

b.

maximum cost edge is added

c.

true

d.

minimum cost edge need not be unique

Discuss
Answer: (c).true
Q48.
A complete undirected graph of n nodes can have maximum ______ spanning trees.

a.

nⁿ⁺¹

b.

nⁿ⁻²

c.

\(\frac{n(n+1)}{2}\)

d.

n

Discuss
Answer: (b).nⁿ⁻²
Q49.
The spanning tree will be maximally acyclic if ____________

a.

one additional edge makes a cycle in the tree

b.

two additional edges makes a cycle in the tree

c.

removing one edge makes the tree cycle free

d.

removing two edges make the tree cycle free

Discuss
Answer: (a).one additional edge makes a cycle in the tree
Q50.
In a maximum spanning tree the weighted graph is of _______

a.

maximum number of edges

b.

maximum number of cyclic trees

c.

minimum number of vertices

d.

maximum weight

Discuss
Answer: (d).maximum weight
Page 5 of 6

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