The maximum number of edges in a minimal graph of diameter 2
Zoltán Füredi · Journal of Graph Theory · 1992
Abstract A graph g of diameter 2 is minimal if the deletion of any edge increases its diameter. Here the following conjecture of Murty and Simon is proved for n < no. If g has n vertices then it has at most n2/4 edges. The only extremum is the complete bipartite graph.