Superpower graphs of finite groups

Ajay Kumar; Lavanya Selvaganesh; Peter J. Cameron; T. Tamizh Chelvam

doi:10.1142/S0219498825502147

Superpower graphs of finite groups

Ajay Kumar, Lavanya Selvaganesh^*, Peter J. Cameron, T. Tamizh Chelvam

^*Corresponding author for this work

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

Abstract

For a finite group G, the superpower graph S(G) of G is an undirected simple graph with vertex set G and two vertices are adjacent in S(G) if and only if the order of one divides the order of the other in G. The aim of this paper is to provide tight bounds for the vertex connectivity, discuss Hamiltonian-like properties of superpower graph of finite non-abelian groups having an element of exponent order.

We also give some general results about superpower graphs and their relation to other graphs such as the Gruenberg–Kegel graph.

Original language	English
Journal	Journal of Algebra and Its Applications
Volume	Online Ready
Early online date	3 Apr 2024
DOIs	https://doi.org/10.1142/S0219498825502147
Publication status	E-pub ahead of print - 3 Apr 2024

Keywords

Superpower graph
Power graph
Hamiltonian cycle
Simple group
Vertex connectivity

Access to Document

10.1142/S0219498825502147

Kumar-2024-Superpower-graphs-of-JAA-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/10.1142/S0219498825502147.
Accepted author manuscript, 383 KB

Cite this

@article{5c9690c6f4c541169867f444de5ad5f3,

title = "Superpower graphs of finite groups",

abstract = "For a finite group G, the superpower graph S(G) of G is an undirected simple graph with vertex set G and two vertices are adjacent in S(G) if and only if the order of one divides the order of the other in G. The aim of this paper is to provide tight bounds for the vertex connectivity, discuss Hamiltonian-like properties of superpower graph of finite non-abelian groups having an element of exponent order.We also give some general results about superpower graphs and their relation to other graphs such as the Gruenberg–Kegel graph. ",

keywords = "Superpower graph, Power graph, Hamiltonian cycle, Simple group, Vertex connectivity",

author = "Ajay Kumar and Lavanya Selvaganesh and Cameron, {Peter J.} and Chelvam, {T. Tamizh}",

note = "Funding: Ajay Kumar is supported by CSIR-UGC JRF, New Delhi, India, through Ref No.: 19/06/2016(i) EU-V/Roll No. 417267. Lavanya Selvaganesh is partially supported by SERB, India, through Grant No. MTR/2018/000254 under the scheme MATRICS. T. Tamizh Chelvam is supported by CSIR Emeritus Scientist Scheme of Council of Scientific and Industrial Research (No.21(1123)/20/EMR-II), Government of India.",

year = "2024",

month = apr,

day = "3",

doi = "10.1142/S0219498825502147",

language = "English",

volume = "Online Ready",

journal = "Journal of Algebra and Its Applications",

issn = "0219-4988",

publisher = "World Scientific Publishing Co. Pte Ltd",

}

TY - JOUR

T1 - Superpower graphs of finite groups

AU - Kumar, Ajay

AU - Selvaganesh, Lavanya

AU - Cameron, Peter J.

AU - Chelvam, T. Tamizh

N1 - Funding: Ajay Kumar is supported by CSIR-UGC JRF, New Delhi, India, through Ref No.: 19/06/2016(i) EU-V/Roll No. 417267. Lavanya Selvaganesh is partially supported by SERB, India, through Grant No. MTR/2018/000254 under the scheme MATRICS. T. Tamizh Chelvam is supported by CSIR Emeritus Scientist Scheme of Council of Scientific and Industrial Research (No.21(1123)/20/EMR-II), Government of India.

PY - 2024/4/3

Y1 - 2024/4/3

N2 - For a finite group G, the superpower graph S(G) of G is an undirected simple graph with vertex set G and two vertices are adjacent in S(G) if and only if the order of one divides the order of the other in G. The aim of this paper is to provide tight bounds for the vertex connectivity, discuss Hamiltonian-like properties of superpower graph of finite non-abelian groups having an element of exponent order.We also give some general results about superpower graphs and their relation to other graphs such as the Gruenberg–Kegel graph.

AB - For a finite group G, the superpower graph S(G) of G is an undirected simple graph with vertex set G and two vertices are adjacent in S(G) if and only if the order of one divides the order of the other in G. The aim of this paper is to provide tight bounds for the vertex connectivity, discuss Hamiltonian-like properties of superpower graph of finite non-abelian groups having an element of exponent order.We also give some general results about superpower graphs and their relation to other graphs such as the Gruenberg–Kegel graph.

KW - Superpower graph

KW - Power graph

KW - Hamiltonian cycle

KW - Simple group

KW - Vertex connectivity

U2 - 10.1142/S0219498825502147

DO - 10.1142/S0219498825502147

M3 - Article

SN - 0219-4988

VL - Online Ready

JO - Journal of Algebra and Its Applications

JF - Journal of Algebra and Its Applications

ER -

Superpower graphs of finite groups

Abstract

Keywords

Access to Document

Fingerprint

Cite this