Forbidden subgraphs in reduced power graphs of finite groups
| Autor: | Ma Xuanlong, Huani Li, Ruiqin Fu |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Functional Analysis
Threshold graph Finite group split graph lcsh:Mathematics High Energy Physics::Lattice General Mathematics High Energy Physics::Phenomenology abelian group lcsh:QA1-939 Dihedral group Vertex (geometry) Nonlinear Sciences::Chaotic Dynamics Combinatorics chordal graph Mathematics::Group Theory Chordal graph reduced power graph Cograph Split graph Abelian group cograph threshold graph Mathematics |
| Zdroj: | AIMS Mathematics, Vol 6, Iss 5, Pp 5401-5420 (2021) |
| ISSN: | 2473-6988 |
| Popis: | 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 $ \langle x\rangle \subset \langle y\rangle $ or $ \langle y\rangle \subset \langle x\rangle $. 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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