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1、漳州师范学院硕士学位论文循环群上4度Bi-Cayley网络的研究姓名：钟玮申请学位级别：硕士专业：计算机应用技术指导教师：陈宝兴20100601ii?Cayley?Cayley?Cayley? ?BiCayley?G?S?(?G?),? ?G?BiCayley?V = G0,1,E = (g,0,sg,1)|g G,s S. BiCayley?Cayley?4?BiCayley?BC(n;s1,s2)?DLG(n;s1,s2)? ?1.?4?Bi Cayley?BC(n;s1,s2)?2.?4?Bi Cayley?BC(n;s1,s2)?3.?4?Bi Cayley?BC(n;s1,s2)?:
2、 Cayley?Bi-Cayley?4?Bi-Cayley?iiiAbstractCayley graphs, which represent a category of symmetric and regular graphsderivable from finite groups, have been shown to be very suitable to serve as in-terconnection network topologies.Many outstanding networks,such as double-loopnetwork,hybercube,star grap
3、h are Cayley graphs.We all know that the Cayley graphhas been studied for a long history,and we have abundance results about it.But wehave 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 generateG
4、 completely, the Bi-Cayley graph BC(G,S) of G with respect to S is defined as thebipartite graph with vertex set V = G0,1 and edge set E = (g,0,sg,1)|g G,s S.Bi-Cayley graphs are generalization of Cayley graphs.Specifically, 4-degreeBi-Cayley graphs of Cyclic Groups are generalization of undirected
5、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 graphsare investigated.2. To get the smallest non-negative solution and the smallest cross solution ,anduse them to calculate the diameter of 4-
6、degree Bi-Cayley graphs of Cyclic GroupBC(n;s1,s2).3.To design the arithmetic to get the shortest path of two point of connected4-degree Bi-Cayley graphs of Cyclic Group BC(n;s1,s2).Key Words: Cayley graph;Bi-Cayley graph;Connectivity;Diameter;arithmetic? ? ?1?2?2?2?”?”?4?4?Bi-Cayley?1?1?(?)? ? ? ?
7、? ?7,8. 1986?SheldonB.Akers?BalakrishnanKrishnamurthy?Cayley?Cayley? ?Cayley?1,9.?4,5,18?Cayley?Cayley?(hypercube)?(double loop network),?(star graph)?Cayley?BiCayley(?Cayley)?Bi Cayley?Cayley?Bi Cayley?Cayley?Cayley? ?BiCayley? ?BiCayley?Cayley?CI?Cayley?19,23,33,39,41,42,43,?Bi Cayley?BCI?Hamilton
8、?2003?24?Bi Cayley?BC(G,S)?A? ?NA(Rrl(G)?34?3?Bi Cayley?An?Bi Cayley?3?(?2? ? ?).2006?6?S1= S S?Bi Cayley?BC(G,S)?Hamilton?2007?36?Bi Cayley? ?Bi Cayley?Cayley?Bi cayley?p?p?pg?BCI?37?G?Cayley?Cay(G,S)?Bi Cayley?BC(G,S)?Bi Cayley?BiCayley?Cayley?BiCayley? ?BiCayley?Cayley?BCI?Cayley?CI?BiCayley?BCI?
9、Cayley?CI?27?2008?27,?Cayley?BCI?30?Zn?2?BiCayley?BC(n;s1,s2)?L?L(2n;l,h,p,q)?DLG(n;s1,s2)?L?L(n;l,h,p,q)?2009?35?BiCayley?Cayley?Bi Cayley?Hamilton?D2p?3p(p?)?Bi Cayley?Hamilton?4?Bi Cayley?Cayley?3?4?Bi Cayley?BC(n;s1,s2)?4?5?4?BiCayley?BC(n;s1,s2)? ?O(log2n).?4?Bi-Cayley?3?2?4?Bi Cayley?Bi Cayley? ?4?Bi Cayley?BC(n;s1,s2)?L?L(2n;l,h,p,q).?2.11?G?S? ?G,?(?Cayley?)?G?S?Cay(G,S),?V = G, E = (g,h)|g,h G,hg1 S? ?g,h G ,?s S,?gs = h?g,h?(g,h)5.?2.1 ?S?G? ?s S ,?s1 S?Cay(G,S)?Cay(G,S),? ?1?Cay
