This paper studies three graph problems with parameters n, the number of nodes, e, the number of edges, and k, the diameter of the graph. Given any two of these three parameters, the problem is to construct a directed graph which minimizes or maximizes the third. The first problem has its origin in a recent study of record allocation in a paged computer system. It is shown how to construct graphs that are optimal for all three problems in some cases and are asymptotically optimal for other cases. The solution of the second problem answers a question raised by Berge in "The Theory of Graphs and its Application," 1962. © 1979.
Hirschberg, D. S., & Wong, C. K. (1979). Upper and lower bounds for graph-diameter problems with application to record allocation. Journal of Combinatorial Theory, Series B, 26(1), 66–74. https://doi.org/10.1016/0095-8956(79)90042-X