Chapter 8, Problem 18E

The digraph in Fig. 8-29 is an example of a tournament digraph. In this example the vertices of the digraph represent five volleyball teams in a round-robin tournament (i.e., every team plays every other team). An arc XY represents that X defeated Y in the tournament. (Note: There are no ties in volleyball.)

a. Which team won the tournament? Explain.

b. Which team came in last in the tournament? Explain.

c. Suppose that you are given the tournament digraph of some tournament. What does the indegree of a vertex represent? What does the outdegree of a vertex represent?

d. If T denotes the tournament digraph for a round-robin tournament with N teams, then for any vertex X in T, the indegree of X plus the outdegree of X = N — 1. Explain why.

Figure 8-29