Research on The Unified Formula of Some Cayley Networks

Cayley graph-connected cycles proposed by S.R.Ohring and F.Sarkar et.al. are constant-degree three network constructed by substituting each node in a degree d Cayley graph(we call base Cayley graph) by a ring Rd of d nodes, each node in Cayley graph-connected cycle has two cycle neighbors and one Cayley neighbor. For this class of graphs there are no known results that help us to prove that some constructions provide always a Cayley graph. We prove that if the base Cayley graph has complete rotation, i.e. it is high symmetrical, then the result graph: Cayley graph-connected cycle is a Cayley graph. Also, we give some simple examples to illustrate our main result.