Hamiltonian connectivity, pancyclicity and 3*-connectivity of matching composition networks

Abstract

In this paper, we discuss many properties of graphs of Matching Composition Networks (MCN) [16]. A graph in MCN is obtained front the disjoint union of two graphs Go and G, by adding a pet-feet matching between V(G(0)) and V(G(1)). We prove that any graph in MCN preserves the hamiltonian connectivity or hamiltonian laceability, and pancyclicity of G(0) and G(1) under simple conditions. In addition, if there exist three internally vertex-disjoint paths between any pair of distinct vertices in G(i) for i is an element of {0, 11, then so it is the case in any graph in MCN. Since MCN includes many well-known interconnection networks as special cases, such as the Hypercube Q(n), the Crossed cube CQ(n), the Twisted cube TQ(n), the Mobius cube MQ(n), and the Hypbercube-like graphs HLn, our results apply to all of the above-mentioned networks.