Two different families of fixed degree regular Cayley networks

Regular Cayley graphs like hypercubes and recently introduced star graphs play an important role in designing interconnection networks for multiprocessing systems; these graphs are regular and the degree of the nodes increases with the size of the graph (the number of nodes) either logarithmically or sub logarithmically. But, from a VLSI design point of view, constant degree networks are more suitable for area efficient layout and there are also important applications the computing nodes in the interconnection network can have only a fixed number of I/O ports. Our purpose in the present paper is to introduce two new families of fixed degree Cayley graphs. The first family has a constant node degree 4 with a connectivity of 4 (thus maximally fault tolerant) and can be viewed as more attractive and efficient alternative of Debruijn graphs. The other family has a constant node degree 3 with a vertex connectivity of 3 (thus maximally fault tolerant), providing a better alternative for Mobius graphs for VLSI implementation in terms of regularity and greater fault tolerance at no additional cost