Question

An n-vertex graph has ______ edges.

(a) n^2

(b) n-1

(c) n*n

(d) n*(n+1)/2

This question was addressed to me in exam.

I would like to ask this question from Properties of Tree topic in chapter Trees of Discrete Mathematics

Answer 1

Correct answer is (b) n-1

For explanation I would say: Suppose G is a connected graph which has no cycles. Every subgraph of G includes at least one vertex with zero or one incident edges. It has n vertices and n-1 edges. Generally, the order-zero graph is not considered to be a tree.