Question

If in a graph G(v,e),|E|=|v|-1 then g is a tree?

Answer 1

Explanation:

Theorem: An undirected graph is a tree iff there is exactly one simple path between each pair of vertices. Proof: If we have a graph T which is a tree, then it must be connected with no cycles. Since T is connected, there must be at least one simple path between each pair of vertices.