Course Graph Theory please provide whole process Thanks D37

Course: Graph Theory

please provide whole process. Thanks.

D37) Let G be a directed graph that satisfies the indegree condition of the Root Theorem as in the preceding problem, and suppose that G contains no directed cycles. Prove that G must be a tree

Solution

Definition for a tree: graph G is a tree if it is connected and has no cycles and a simple cycle is formed if any edge is added to G, but is not connected if any single edge is removed from G.

if we show that a graph with no cycles and |V|1 edges must be connected?

Here in our problem gave:

   Let G be a directed graph that satisfies the indegree condition and G contains no directed cycles.

By indegree condition the edges are |V|1 edges must be connected.

   so that it is a tree.