A forest is an unconnected graph that is a disjoint union of

A forest is an unconnected graph that is a disjoint union of trees. If G is an n-vertex forest of t trees, how many edges does it have?

A Forest is a disjoint union of trees

Given

G is n-vertex forest of t trees

If ti is a non-empty tree,

Then |E(ti)|=|V(ti)|-1 ……(1)

As given there are t trees that is t1,t2,…..tt,

Let each ti has ni vertices.

By adding we have

|E(G)|= Sum of edges of all trees

Use the equation (1) here

|E(G)| = Sum of all vertices of Ti -1

= sum of all ni -1

Hence no of edges of G = no of vertices of G - t

where t is no of trees.