循环群上4度b-cayley网络的研究.pdf

ii Cayley Cayley Cayley Bi −Cayley G S ( G ), G Bi − Cayley V = G × {0, 1}, E = {([g, 0], [sg, 1])|g ∈ G, s ∈ S}. Bi − Cayley Cayley 4 Bi −Cayley BC (n; ±s , ±s ) 1 2 DLG(n; ±s , ±s ) 1 2 1. 4 Bi − Cayley BC (n; ±s , ±s )  1 2 2. 4 Bi − Cayley BC (n; ±s , ±s ) 1 2 3. 4 Bi − Cayley BC (n; ±s , ±s ) 1 2 : Cayley Bi-Cayley 4 Bi-Cayley ℄ iii Abstract Cayley 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 investi