Question

Is the statement ""For every natural number n ≥ 1 there exists a directed graph of n vertices for which every vertex has an indegree equal to its outdegree"" TRUE or FALSE?

Answer 1

Answer:

The given statement is false.

Step-by-step explanation:

Reason

let D be a directed graph with 'n' no of vertices and 'E' edges.

where 'n'=1.  thus D =(n,E).

In degree: in directed graph the number of incoming edges on a vertex is known as indegree.

it is denoted as deg ⁺(n).

And now we know that in a directed graph

if deg ⁻(n)= deg ⁺(n) for each vertex n.