Undirected loop networks
Sheng Chen, Xing‐De Jia · Networks · 1993
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, ±a2 …, ±ak} 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.