Forbidden subgraphs in reduced power graphs of finite groups

AIMS Mathematics

Huani Li¹  Xuanlong Ma²  Ruiqin Fu² 

[1] 1. Academy of Freshmen, Xi'an Technological University, Xi'an 710021, China;2. School of Science, Xi'an Shiyou University, Xi'an 710065, China;

关键词: reduced power graph;    split graph;    cograph;    chordal graph;    threshold graph;    abelian group;   

DOI  :  10.3934/math.2021319

来源: DOAJ

【 摘 要 】

Let G be a finite group. The reduced power graph of G is the undirected graph whose vertex set consists of all elements of G, and two distinct vertices x and y are adjacent if either ⟨x⟩⊂⟨y⟩ or ⟨y⟩⊂⟨x⟩. In this paper, we show that the reduced power graph of G is perfect and characterize all finite groups whose reduced power graphs are split graphs, cographs, chordal graphs, and threshold graphs. We also give complete classifications in the case of abelian groups, dihedral groups, and generalized quaternion groups.

【 授权许可】

Unknown