一类Frobenius图网络  

A Class of Frobenius Graph Interconnection Network

作　　者：蔡晓霞 孔祥志 王燕[1] CAI Xiao-xia;KONG Xiang-zhi;WANG Yan(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2020年第3期253-255,282,共4页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11671347,61771019);山东省自然科学基金资助项目(ZR2017MAO022).

摘　　要：构造了一类有限域上向量空间加法群的凯莱图,它是对超立方体图的一种自然推广.证明了这类图是哈密尔顿连通和哈密尔顿可分解的、具有最大的点连通度而且既是超点也是超边连通的,因此它也是一个非常好的网络模型.更进一步,在某些条件下证明了它还是一类Frobenius图,因此这类图比一般的凯莱图对称性更强.We define a class of Cayley graphs based on vector spaces over finite fields.It is a natural generalization of hypercubes.We prove that these graphs are Hamilton connected and Hamilton decomposable,have the maximum vertex connectivity,super-vertex and super-edge connectivity.So,it is indeed a class of“good”interconnection network model.Moreover,we show that under some conditions these graphs are also Frobenius graphs.Therefore,they are more symmetric than general Cayley graphs.

关 键 词：FROBENIUS群 凯莱图 Frobenius图 网络 

分 类 号：O157.5[理学—数学]