Undirected loop networks

Abstract

Abstract Let M, d , and k be positive integers. We say that M is feasible with respect to d and k if there exists a set A = {0, ± 1, ±a 2 …, ±a k } such that the Cayley graph associated with Z/(M) and A has diameter less than or equal to d . Such a Cayley graph is a model for undirected loop communication networks. Denote M(d, k) the maximal feasible number M with respect to d and k . In the paper, an explicit formula for M ( d , 2) is obtained. Also, when k ≧ 3, a lower bound for M(d, k) is established. © 1993 by John Wiley & Sons, Inc.