广义四元数群上的3度1-匹配bi-Cayley图  

Cubic One-Matching Bi-Cayley Graphs over Generalized Quaternion Group

作　　者：李圆 王丽[1] 吕宝栋 Li Yuan;Wang Li;Lv Baodong(School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454000,China)

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《洛阳师范学院学报》2020年第5期14-17,共4页Journal of Luoyang Normal University

摘　　要：称一个图是群H上的bi-Cayley图,如果它有一个同构于H的半正则自同构群且作用在顶点集上恰有两个轨道.如果连接这两个轨道的边所诱导的二部图是一个完美匹配,称此图是1-匹配bi-Cayley图.讨论了广义四元数群Q 36上的两类3度1-匹配bi-Cayley图的自同构群,并证明了这两类图的点传递性,边传递性和弧传递性.A graph is called a bi-Cayley graph on group H which admits a semi-regular auto-morphism group isomorphic to H with two orbits,and is a one-matching bi-Cayley if the bipartite graph induced by the edges joining these two orbits is a perfect matching.The automorphism groups of two classes of cubic one-matching bi-Cayley graphs on the generalized quaternion group Q 36 are discussed.In addition,the vertex transitivity,edge transitivity and arc transitivity of these two classes of graphs are proved.

关 键 词：广义四元数群 bi-Cayley图 自同构群 

分 类 号：O157.5[理学—数学] O152.5[理学—基础数学]