论文标题
在非构形群上的两个图形家族
Two families of graphs that are Cayley on nonisomorphic groups
论文作者
论文摘要
许多作者研究了何时可以将图表表示为多个非同构组上的Cayley图的问题。迄今为止的工作集中在一些特殊情况下：当小组为$ p $ groups时；当小组有订单$ PQ $时；当Cayley图形正常时；或当小组都是Abelian时。在本文中，我们构建了两个无限的图表，每个图都在阿贝里安群体和一个非阿布尔群体上。这些家庭包括其他结果中未出现的最小示例。
A number of authors have studied the question of when a graph can be represented as a Cayley graph on more than one nonisomorphic group. The work to date has focussed on a few special situations: when the groups are $p$-groups; when the groups have order $pq$; when the Cayley graphs are normal; or when the groups are both abelian. In this paper, we construct two infinite families of graphs, each of which is Cayley on an abelian group and a nonabelian group. These families include the smallest examples of such graphs that had not appeared in other results.
