Hamiltonian Connectedness of Mesh Networks with Wraparound Edges

랩어라운드 에지를 갖는 메쉬 연결망에서의 해밀톤 연결성

In this paper, we consider the hamiltonian properties of m ${\times}$ n mesh networks with two wrap-around edges. We describe sufficient condition that at least two edges should be added to a mesh to make it hamiltonian-connected. We propose two graphs, M1(ｍ,n) and M2(ｍ,n). These are obtained by adding one and two edges respectively in the ｍ${\times}$ｎ mesh. We show the hamiltonian properties of M1(ｍ,n) and prove that M2(m, n) is hamiltonian-connected using the hamiltonian properties of M1(ｍ,n).