Top | MCQs on Graph Traversals with Answers | Question 27

For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?

(A)

v= e-1

(B)

e= v-2

(C)

v=e+1

(D)

None

Answer: (C)
Explanation:

For a given graph G is connected, has no cycles (also called acyclic), and has v – 1 edges. Since G is connected and has no cycles, and the number of edges (e) is v – 1, it satisfies the definition of a tree. Trees are fundamental data structures in graph theory and have important applications in computer science and various other fields.

The number of edges e= v-1 or v= e+1.

Hence Option(C) is the correct answer.

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