两类可解群双Cayley图的Hamilton性  

Hamiltonian Property in Bi-Cayley Graphs of Two Kinds of Finite Solvable Groups

作　　者：王梦雨[1] 徐尚进[1] 谢金华 杨霞 WANG Meng-yu;XU Shang-jin;XIE Jin-hua;YANG Xia(College of Mathematics and Information Science,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西师范学院学报（自然科学版）》2018年第1期8-12,共5页Journal of Guangxi Teachers Education University(Natural Science Edition)

基　　金：国家自然科学基金(10961004;11361006;11461004);广西自然科学基金(2015GXNSFAA139001)

摘　　要：该文研究双Cayley图Γ∶=BCay(G,S)的Hamilton性.通过Γ所对应的(单)Cayley图,G的商群的双Cayley图,乃至Γ的导出子图的Hamilton圈来构造Γ的Hamilton圈.获得了关于pq阶群(其中p>q>2是素数)和广义四元数群Q4r(r为奇素数)双Cayley图Hamilton性的一些结果.For a bi-Cayley graphΓ∶=BCay(G,S),its Hamiltonian property is researched in this paper,and its Hamiltonian cycles are constructed by those Hamiltonian cycles of the corresponded(single)Cayley graph,of the bi-Cayley graph on G’s quotient group,and of its induced subgraphs.Furthermore,some results about the Hamiltonian property of bi-Cayley graphs on the group which has order pq(p>q>2 are prime)or on the generalized quaternion group Q4r(r is odd prime)are obtained.

关 键 词：双CAYLEY图 HAMILTON图 pq阶群 广义四元数群 

分 类 号：O157.5[理学—数学]