graph theory

Question

complete directed graph with 8 vertices has 28 edges

this statement is true or false

plese explain?

Comments

False. It should be 56. Formula will be N(N-1). Where N =number of vertices.

• Complete directed graphs are simple directed graphs where each pair of vertices is joined by a symmetric pair of directed arcs (it is equivalent to an undirected complete graph with the edges replaced by pairs of inverse arcs). It follows that a complete digraph is symmetric.

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Source of the formula?

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I generated the formula from the definition.

Answer 1

A complete undirected graph of 8 vertices will have ($\binom{8}{2}$) edges which comes to 28. Now since the graph is directed hence in place of each edge in the undirected version we will have an edge in either direction in the directed version. Hence the total number of edges would be 56.