Question

A league of 19 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played? Justify your answer using a graph model—say what the vertices and edges of your graph represent, and what (if any) theorems you use. (Upload your file below.)

Answer 1

$_{19}\text{C}_2=171$ games. For your graph, put 19 vertices and connect them all together once. The vertices are the teams and the edges are the games.