Ring embedding in faulty honeycomb rectangular torus

Assume that m and n are positive even integers with n 4. The honeycomb rectangular torus HReT(m,n) is recognized as another attractive alternative to existing torus interconnection networks in parallel and distributed applications. It is known that any HReT(m,n) is a 3-regular bipartite graph. We prove that any HReT(m,n) − e is hamiltonian for any edge e ∈ E(HReT(m,n)). Moreover, any HReT(m,n)− F is hamiltonian for any F = {a, b} with a ∈A and b ∈ B where A and B are the bipartition of HReT(m,n), if n 6 or m= 2.  2002 Elsevier Science B.V. All rights reserved.