3p阶群的3度bi-Cayley图
Cubic bi-Cayley graphs over a group of order 3p
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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2个轨道. 分类了一类3p(p为奇素数)阶非交换群上的所有3度bi-Cayley图,并证明3度点传递bi-Cayley图一定同构于一个Cayley图,同时给出了这类图的全自同构群.Abstract: A graph is said to be a bi-Cayley graph over a group H, if it admits H as a semiregular automorphism group with two orbits of equal size. We classify all cubic bi-Cayley graphs over a nonabelian group of order 3p(p is odd prime). We prove that the cubic vertex-transitive bi-Cayley graphs must be isomorphic to Cayley graphs. In addition, the automorphism group of the graph is discussed.