On symmetries of Cayley graphs and the graphs underlying regular maps
On symmetries of Cayley graphs and the graphs underlying regular maps
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DOI：
10.1016/j.jalgebra.2008.04.016
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发表时间：
2009-06
影响因子：
0.9
通讯作者：
M. Conder
中科院分区：
文献类型：
--
作者：
M. Conder
根据定义，凯莱图是顶点传递的，正则或定向正则映射（在曲面上）下面的图是弧传递的。本文解决了此类图的自同构群可以有多大的问题。特别是，它展示了如何构造 5 弧传递的 3 价凯莱图（回答 Cai Heng Li 的问题），以及对于所有 t>0 的 7 弧传递的价 3t+1 凯莱图。可以采用相同的方法来考虑正则或定向正则图的基础图，从而对具有 1-、4-或 5-弧-正则 3 价基础图的所有此类图进行分类（回答 Cheryl Praeger 和 Sanming Zhou 的问题）。
By definition, Cayley graphs are vertex-transitive, and graphs underlying regular or orientably-regular maps (on surfaces) are arc-transitive. This paper addresses questions about how large the automorphism groups of such graphs can be. In particular, it is shown how to construct 3-valent Cayley graphs that are 5-arc-transitive (in answer to a question by Cai Heng Li), and Cayley graphs of valency 3t+1 that are 7-arc-transitive, for all t>0. The same approach can be taken in considering the graphs underlying regular or orientably-regular maps, leading to classifications of all such maps having a 1-, 4- or 5-arc-regular 3-valent underlying graph (in answer to questions by Cheryl Praeger and Sanming Zhou).