Two new families of large compound graphs

Abstract

A question of special interest in graph theory is the design of large graphs. Specifically, we want to find constructions of graphs with order as large as possible for a given degree and diameter D. Two generalizations of two large compound graphs are proposed in this article. Three particular cases of these families of graphs presented here allow us to improve the order for the entries (15, 7), (13, 10), and (15, 10) in the table of the largest known ( , D)-graphs.