Finite groups whose commuting graph is split

Xuanlong Ma; Peter J. Cameron

doi:10.21538/0134-4889-2024-30-1-280-283

Finite groups whose commuting graph is split

Xuanlong Ma^*, Peter J. Cameron

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

As a contribution to the study of graphs defined on groups, we show that for a finite group G the following statements are equivalent: the commuting graph of G is a split graph; the commuting graph of G is a threshold graph; either G is abelian, or G is a generalized dihedral group D(A)=⟨A,t:(∀a∈A)(at)²=1⟩ where A is an abelian group of odd order.

Original language	English
Pages (from-to)	280-283
Journal	Trudy Instituta Matematiki i Mekhaniki UrO RAN
Volume	30
Issue number	1
DOIs	https://doi.org/10.21538/0134-4889-2024-30-1-280-283
Publication status	Published - 4 Mar 2024

Keywords

Commuting graph
Split graph
Threshold graph
Generalized dihedral group

Access to Document

10.21538/0134-4889-2024-30-1-280-283

Ma-2024-Finite-groups-whose-commuting-Mekhaniki-UrO-RAN-AAM-CCBY
Copyright © 2024 the Authors. This work has been made available online in accordance with the Rights Retention Strategy This accepted manuscript is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The final published version of this work is available at https://doi.org/10.21538/0134-4889-2024-30-1-280-283.
Accepted author manuscript, 222 KBLicence: CC BY

Cite this

@article{691ba0d352d94132b744c390ba61ae83,

title = "Finite groups whose commuting graph is split",

abstract = "As a contribution to the study of graphs defined on groups, we show that for a finite group G the following statements are equivalent: the commuting graph of G is a split graph; the commuting graph of G is a threshold graph; either G is abelian, or G is a generalized dihedral group D(A)=⟨A,t:(∀a∈A)(at)2=1⟩ where A is an abelian group of odd order.",

keywords = "Commuting graph, Split graph, Threshold graph, Generalized dihedral group",

author = "Xuanlong Ma and Cameron, {Peter J.}",

year = "2024",

month = mar,

day = "4",

doi = "10.21538/0134-4889-2024-30-1-280-283",

language = "English",

volume = "30",

pages = "280--283",

journal = "Trudy Instituta Matematiki i Mekhaniki UrO RAN",

issn = "0134-4889",

publisher = "Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences",

number = "1",

}

TY - JOUR

T1 - Finite groups whose commuting graph is split

AU - Ma, Xuanlong

AU - Cameron, Peter J.

PY - 2024/3/4

Y1 - 2024/3/4

N2 - As a contribution to the study of graphs defined on groups, we show that for a finite group G the following statements are equivalent: the commuting graph of G is a split graph; the commuting graph of G is a threshold graph; either G is abelian, or G is a generalized dihedral group D(A)=⟨A,t:(∀a∈A)(at)2=1⟩ where A is an abelian group of odd order.

AB - As a contribution to the study of graphs defined on groups, we show that for a finite group G the following statements are equivalent: the commuting graph of G is a split graph; the commuting graph of G is a threshold graph; either G is abelian, or G is a generalized dihedral group D(A)=⟨A,t:(∀a∈A)(at)2=1⟩ where A is an abelian group of odd order.

KW - Commuting graph

KW - Split graph

KW - Threshold graph

KW - Generalized dihedral group

UR - http://doi.org/10.21538/0134-4889

UR - https://trimm.uran.ru/issues

U2 - 10.21538/0134-4889-2024-30-1-280-283

DO - 10.21538/0134-4889-2024-30-1-280-283

M3 - Article

SN - 0134-4889

VL - 30

SP - 280

EP - 283

JO - Trudy Instituta Matematiki i Mekhaniki UrO RAN

JF - Trudy Instituta Matematiki i Mekhaniki UrO RAN

IS - 1

ER -

Finite groups whose commuting graph is split

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this