Gonitzoggo has arranged a Football tournament where there are $8$ football teams. Eight football teams play matches against each other in such a way that no two teams meet twice and no three teams play all of the three possible matches; for example, If $A$ plays with $B$ and $B$ plays with $C$, $C$ doesn’t play with $ A$. Find out the largest total number of matches possible in the tournament.
If we consider it as a graph, where the teams are nodes and an edge connecting two nodes refer to a game between them, it implies that this graph must not have any triangles. What is the maximum amount of edges possible like this for $8$ nodes?
Gonitzoggoβ