Embedding a fault-free hamiltonian cycle in a class of faulty generalized honeycomb tori

Generalized honeycomb torus (GHT) is recognized as an attractive alternative to existing torus interconnection networks in parallel computing systems. Assume that m and d are integers with m ? 2 and d ? 8. This paper addresses the fault-tolerant hamiltonicity of GHT(m, 2d, d) with fault set F = {(w, y), (x, y)}, where w < x, w + y is even and x + y is odd. We show that such a faulty GHT is hamiltonian by presenting a systematic method for constructing a fault-free hamiltonian cycle. This result reveals another appealing feature of GHTs.