The dilating method to obtain dense cayley digraphs on finite abelian groups

Abstract

A geometric method for obtaining an infinite family of Cayley digraphs of constant density on finite abelian groups is presented. The method works for any given degree d ≥ 2, and it is based on consecutive dilates of a minimum distance diagram associated with a given initial Cayley digraph. The method is used to obtain infinite families of dense or asymptotically dense Cayley digraphs. In particular, for degree d = 3, the first explicit infinite family of maximum known density d = 0.084 is obtained.