Study On 4-degree Bi-Cayley Graphs Of Cyclic Group

Cay ley graphs, which represent a category of symmetric and regular graphs derivable from finite groups, have been shown to be very suitable to serve as in-terconnection network topologies.Many outstanding networks,such as double-loop network,hybercube,star graph are Cayley graphs.We all know that the Cayley graph has been studied for a long history,and we have abundance results about it.But we have few results about Bi-Cayley still now.For a finite group G and a set of gener-ating elements S(possibly,it contains the identity element)of G,which can generate G completely, the Bi-Cayley graph BC(G,S) of G with respect to S is defined as the bipartite graph with vertex set V=G×{0,1} and edge set E={([g,0], [sg, 1])|g∈G, s∈S}.Bi-Cayley graphs are generalization of Cayley graphs.Specifically,4-degree Bi-Cayley graphs of Cyclic Groups are generalization of undirected double-loop net-works.In this paper we maily study the following three questions.1. The necessary and sufficient condition of the connectivity of Bi-Cayley graphs are investigated.2. To get the smallest non-negative solution and the smallest cross solution,and use them to calculate the diameter of 4-degree Bi-Cayley graphs of Cyclic Groups BC(n;±s1,±s2).3.To design the arithmetic to get the shortest path of two point of connected 4-degree Bi-Cayley graphs of Cyclic Groups BC(n;±s1,±s2).