UNDIRECTED LOOP NETWORKS

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 ..., +/-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 greater-than-or-equal-to 3, a lower bound for M(d, k) is established.