Fault-tolerant Hamiltonian connectivity of 2-tree-generated networks

Interconnection networks are often modeled by finite graphs. The vertices of the graph represent the nodes of the network (processing elements, memory modules or switches), and the edges correspond to communication lines. There are many advantages in using Cayley graphs as models for interconnection networks. In this paper we consider a class of Cayley graphs that are generated by certain 3-cycles on the alternating group A_n. These graphs are generalizations of the alternating group graph AG_n. We look at the case when the 3-cycles form a “tree-like structure”, and analyze the fault-Hamiltonian connectivity of such graphs. We prove that these graphs are (2n−7)-fault-tolerant Hamiltonian connected.