Graphs with small diameter after edge deletion (Q1199416)

Let \(g(n,D)\) be a minimum number of edges of a graph on \(n\) vertices such that after removing any edge the resulting graph is of diameter at most \(D\). The problem of finding the values of \(g\) is a special case of a question asked by \textit{K. Vijayan} and \textit{U. S. R. Murty} [Sankhyā, Ser. A 26, 299-302 (1964; Zbl 0134.433)]. In the paper \(g(n,D)\) is determined for general \(n\) and \(D\).