Gossiping and routing in undirected triple-loop networks

Abstract

Given integers n ≥ 7 and a, b, c with 1 ≤ a,b,c ≤ n - 1 such that a,n - a,b,n - b,c,n - c are pairwise distinct, the (undirected) triple-loop network TLn(a,b,c) is the degree-six graph with vertices 0,1,2,..., n - 1 such that each vertex x is adjacent to x ± a, x ± b, and x ± c, where the operation is modulo n. It is known that the maximum order of a connected triple-loop network of the form TLn(a,b,n - (a + b)) with given diameter d ≥ 2 is nd = 3d2 + 3d + 1, which is achieved by TLnn = TLnd(1,3d+1,3d2-1). Inthis article, westudythe routing and gossiping problems for such optimal triple-loop networks under the store-and-forward, all-port, and full-duplex model, and prove that they admit "per..