中心图与中间图的自同构群与可区分着色
组合数学
2026-04-09 v2 群论
摘要
设 为简单、有限、连通且无向的图。 的中间图 是在 的细分图 中，将位于 相邻边上的细分顶点对连接后得到的； 的中心图 是在 中将 的所有不相邻顶点连接后得到的。我们证明，若 的阶数至少为 4，则 、 和 （作为抽象群）同构，并受 Kalinowski、Pilsniak 和 Wozniak 于 2016 年提出的算法启发，应用这些结果获得了 和 的可区分数与可区分指数的新上界。
引用
@article{arxiv.2507.16301,
title = {Automorphism groups and Distinguishing Colorings of Central and Middle Graphs},
author = {Amitayu Banerjee and Alexa Gopaulsingh and Zalán Molnár},
journal= {arXiv preprint arXiv:2507.16301},
year = {2026}
}
备注
In this revised version, written by the first author, proofs of Propositions 3.2 and 3.3 that were not included in the previous version have been added. Some results have been rewritten and improved, and those not directly related to distinguishing colorings of central and middle graphs have been removed. The manuscript includes five figures