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 ≥ 2 and even n ≥ 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 e ∈ E(GHT(m, n, n/2)). Moreover, any GHT(m, n, n/2) − F is Hamiltonian for any F = {u, v} with u ∈ B and v ∈ W , where B and W are the bipartition of V (GHT(m, n, n/2)) if and only if n ≥ 6 or m = 2, n ≥ 4.

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