Ring embedding in faulty generalized honeycomb torus - GHT(m, n, n/2)

Abstract

The honeycomb torus HT(m) is an attractive architecture for distributed processing applications. For analysing its performance, a symmetric generalized honeycomb torus, GHT(m, n, n/2), with m epsilon 2 and even n epsilon 4, where m+n/2 is even, which is a 3-regular, Hamiltonian bipartite graph, is operated as a platform for combinatorial studies. More specifically, GHT(m, n, n/2) includes GHT(m, 6m, 3m), the isomorphism of the honeycomb torus HT(m). It has been proven that any GHT(m, n, n/2)-e is Hamiltonian for any edge eE(GHT(m, n, n/2)). Moreover, any GHT(m, n, n/2)-F is Hamiltonian for any F={u, v} with uB and vW, where B and W are the bipartition of V(GHT(m, n, n/2)) if and only if n epsilon 6 or m=2, n epsilon 4.