Equality of Power Graphs, Enhanced Power Graphs and Commuting Graphs on Semigroups

被引：0
|
作者：
Wang, Yanhui [1 ]
Lu, Xue [1 ]
Guo, Xiuyun [1 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China
来源：
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS | 2024年 / 48卷 / 04期
关键词：
Completely simple semigroup; A semilattice of semigroups; Power graph; Enhanced power graph; Commuting graph;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper focuses on three kinds of graphs built from semigroups: power graphs, enhanced power graphs and commuting graphs. Let S be a semigroup constructed in a prescribed way from a semigroup T. We show in particular instances that pairs of these graphs built over S coincide precisely when the same pairs built over T coincide. This is true, for example, when S is a completely simple semigroup and T is a maximal subgroup. We give several other instances of this phenomenon. In addition, we give counterexamples to show that equality for an arbitrary pair of these three graphs does not always pass between semigroups and their maximal subgroups.
引用
收藏
页码：579 / 595
页数：17
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