二面体群的双凯莱图的匹配可扩性（英文）  

The extendabilityof bi-Cayley graphs of dihedral groups

作　　者：高兴[1] 吕华众 王维忠[3] 

机构地区：[1]兰州大学数学与统计学院应用数学与复杂系统重点实验室,甘肃兰州730000 [2]电子科技大学数学科学学院,四川成都611731 [3]兰州交通大学数学系,甘肃兰州730070

出　　处：《浙江大学学报（理学版）》2015年第5期526-528,共3页Journal of Zhejiang University（Science Edition）

基　　金：Supported by the National Natural Science Foundation of China(11201201);the Natural Science Foundation of Gansu Province(1308RJZA112);the Fundamental Research Funds for the Central Universities(lzujbky-2015-76)

摘　　要：令G为有限群,S为G的非空有限子集,G关于S的双凯莱图BC(G,S)是一个二部图,其顶点集是G×{0,1},边集是{(g,0)(sg,1)|g∈G,s∈S}.若有完美匹配的连通图Γ至少有2n+2个顶点,且每一个大小为n的匹配都可以扩充为一个完美匹配,则称此完美匹配的连通图Γ是n-可扩的,并对二面体群的双凯莱的2-可扩性进行了刻画.Let Gbe a finite group and Sa nonempty subset（possibly containing the identity element）of G.The biCayley graph BC（G,S）of G with respect to Sis defined as the bipartite graph with vertex set G×{0,1}and edge set{（g,0）（sg,1）｜g∈G,s∈S}.A connected graphΓadmitting aperfect matching is called n-extendable wheneverΓhas at least 2n＋2vertices,and every matching of size ncan be extended to a perfect matching ofΓ.The 2-extendable bi-Cayley graphs of dihedral groups are characterized.

关 键 词：双凯莱图 可扩性 二面体群 

分 类 号：O157.5[理学—数学]