On the number of graphs and h-hypergraphs with bounded diameter Original Research Article

In this paper some asymptotic formulas for the number of graphs, digraphs or h-hypergraphs of order n and diameter equal to k are surveyed. In the case of h-hypergraphs (h⩾3) they depend on the parity of k and are more precise for k⩾5. As a consequence, it is deduced that for k⩾2, almost every graph, digraph or h-hypergraph with diameter k or k+1 has diameter exactly k. Some open problems and conjectures are proposed.