有限群增强幂图中的禁用子图
组合数学
2024-04-15 v5
摘要
群的增强幂图是以群中所有元素为顶点集的简单图，若任意一对顶点生成一个循环子群则相邻。本文分类了所有增强幂图为分裂图与阈值图的有限群。我们也分类了所有增强幂图为弦图与余图的有限幂零群。最后，给出了一些增强幂图为弦图与余图的非幂零群族。这些结果部分回答了 Peter J. Cameron 提出的一个问题。
引用
@article{arxiv.2104.04754,
title = {Forbidden subgraphs in enhanced power graphs of finite groups},
author = {Xuanlong Ma and Samir Zahirović and Yubo Lv and Yanhong She},
journal= {arXiv preprint arXiv:2104.04754},
year = {2024}
}
备注
This paper has been accepted for publication in Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'aticas. Note that this is not a finally version. Its finally version will soon appear in the journal's homepage