Wide Diameter of Cayley Digraphs of Finite Cyclic Groups

Abstract

According to recent studies, communication networks built on extremal Cayley digraphs of finite cyclic groups have many advantages over that based on n-cubes. Extremal Cayley digraphs have been studied extensively in recent years. In this paper, we prove, for every positive integer k, that the k-wide diameter of the Cayley digraph Cay(Zm, A) is at most diam(Cay(Zm, A)) + 1 if A is an "m-ideal" set of k positive integers.