蜂窝环面图的对称性
Symmetries of the Honeycomb toroidal graphs
AI总结：
本文针对蜂窝环面图这一参数化三正则 Cayley 图族，确定了每个图的完整自同构群，从而解决 Alspach 综述中提出的两个研究问题。
摘要：
蜂窝环面图是由一组三个参数确定的三正则图族，过去三十年来一直受到数学家和计算机科学家的研究。它们都可以嵌入环面，并且等同于广义二面体群关于一组三个反射的三正则 Cayley 图。在最近的一篇综述论文中，B. Alspach 汇集了关于这一引人入胜的图族的大多数已知结果，并提出了若干与之相关的研究问题。本文通过确定每个蜂窝环面图的完整自同构群，解决了其中两个问题。
英文摘要：
{\em Honeycomb toroidal graphs} are a family of cubic graphs determined by a set of three parameters, that have been studied over the last three decades both by mathematicians and computer scientists. They can all be embedded on a torus and coincide with the cubic Cayley graphs of generalized dihedral groups with respect to a set of three reflections. In a recent survey paper B. Alspach gathered most known results on this intriguing family of graphs and suggested a number of research problems regarding them. In this paper we solve two of these problems by determining the full automorphism group of each honeycomb toroidal graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
