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.
Citation
Kumar , A , Selvaganesh , L , Cameron , P J & Chelvam , T T 2024 , ' Superpower graphs of finite groups ' , Journal of Algebra and Its Applications , vol. Online Ready . https://doi.org/10.1142/S0219498825502147
Publication
Journal of Algebra and Its Applications
Status
Peer reviewed
ISSN
0219-4988Type
Journal article
Description
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.Collections
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