将群自同构与Cayley图的保色自同构复合
Composing group automorphisms with colour-preserving automorphisms of Cayley graphs
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中文总结 AI 辅助
本文证明连通有限Cayley图的保色置换自同构在阶为奇数或无平方因子数时可分解为群自同构与保色图自同构的复合，并推广到不同图之间的同构。
中文摘要 AI 辅助
我们证明，若φ是连通有限Cayley图的保色置换自同构，且该Cayley图的阶为奇数或无平方因子数，则φ可表示为某个群自同构与一个保色图自同构的复合。此外，对于两个不同Cayley图之间的同构，我们也建立了若干类似的结果。
英文摘要
We show that if $φ$ is a colour-permuting automorphism of a connected, finite Cayley graph, and the order of the Cayley graph is either odd or square-free, then $φ$ is the composition of a group automorphism and a colour-preserving graph automorphism. Some analogous results are also established for isomorphisms between two different Cayley graphs.
