Deformed Honeycomb Tori

Abstract

Assume that m, n and s are integers with m >= 2, n >= 4, 0 < s < n and s is of the same parity of m. The generalized honeycomb tori GHT (m, n, s) have been recognized as an attractive architecture to existing torus interconnection networks in parallel and distributed applications. Among the various families of graphs of GHT (m, n, s), numerous studies are devoted to honeycomb hexagonal torus HT(n) due to its nice symmetrical structure. Although each vertex of HT(n) is described by a three-dimensional coordinate (x, y, z), the graph grows uniformly in the three directions. In this article, we propose a new class of graphs extended from HT (n), namely, deformed honeycomb torus DHT (h, l, r). DHT (h, l, r) is defined to allow the graph to grow in the three independent dimensions. We prove that this more general class of graphs still remains a subset of the generalized honeycomb torus. Furthermore, we have a concrete correspondence between any DHT(h, l, r) and the associated GHT (m, n, s).