The hamiltonicity of generalized honeycomb torus networks

•Previous proofs of hamiltonicity of GHT(m,n,d) are not sufficient when m is odd.•We propose construction procedures of hamiltonian cycles in GHT(m,n,d) with odd m.•GHT(m,n,d) is isomorphic to GHT(m,n,n−d). Yang et al. (2004) [8] proved that the generalized honeycomb torus GHT(m,n,d) is hamiltonian, but their proofs are not sufficient when the width m is odd. In this paper, we propose a series of procedures for constructing hamiltonian cycles in generalized honeycomb tori, which apply to every instance of GHT(m,n,d) with odd width m.