Generalized matching networks and their properties

In this paper, we introduce two kinds of graphs: the generalized matching networks (GMNs) and the recursive generalized matching networks (RGMNs). The former generalize the hypercube-like networks (HLNs), while the latter include the generalized cubes and the star graphs. We prove that a GMN on a family of k-connected building graphs is (k + 1)-connected. We then prove that a GMN on a family of Hamiltonian-connected building graphs having at least three vertices each is Hamiltonian-connected. Our conclusions generalize some previously known results.