Discret mathematics/Groups (football)/4/Isomorphic/Invariants/Classification/Exercise

A football group of a Europe or World championship consists of four teams, and every team plays versus every other team. A game may end in a tie or with a victory for one of the two teams. We are interested in the discrete structure of a football group, which we describe with the help of a directed graph. A victory of ${}A$ over ${}B$ is described by an arrow from ${}A$ to ${}B$ (and a tie is described by no arrow).

Define a concept of an isomorphism for football groups. Classify the football groups along suitable numeric invariants. How many football groups do exist? When can we deduce from the isomorphism class the order in the table?

Create a solution