A simple connected digraph in which there is exactly one dir

A simple, connected digraph in which there is exactly one directed edge between every pair of vertices is called a tournament digraph.

How many tournament digraphs on n labeled vertices contain two vertices, one of in-degree zero and one of out-degree zero?

Solution

A simple, connected digraph in which there is exactly one directed edge between every pair of vertices is called a tournament digraph.

A vertex with an indegree of 0 is called a source (since one can only leave it) and a vertex withan outdegree of 0 is called a sink (since one cannot leave it). It is relatively easy to see that a directed graph with no cycles has atleast one source and one sink.

In a directed graph, vertices have both \"indegrees\" and \"outdegrees\". the indegree of a vertex is the number of arcs leading to that vertex, and the outdegree of a vertex is the number of arcs leading away from that vertex.

the no. of tournament digraphs on n labeled vertices contain two vertices, one of in- degree zero and one of out-degree zero is n-1.