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Solvable conjugacy class graph of groups

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Bhowal_2023_DM_Solvable_conjugacy_CC.pdf (301.0Kb)
Date
08/2023
Author
Bhowal, Parthajit
Cameron, Peter J.
Nath, Rajat Kanti
Sambale, Benjamin
Keywords
Clique number
Solvable group
Graph
Girth
Q Science
Mathematics(all)
T-DAS
MCP
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Abstract
In this paper we introduce the graph Gamma_sc(G) associated with a group G, called the solvable conjugacy class graph (abbreviated as SCC-graph), whose vertices are the nontrivial conjugacy classes of G and two distinct conjugacy classes C, D are adjacent if there exist x in C and y in D such that x and y generate a solvable group. We discuss the connectivity, girth, clique number, and several other properties of the SCC-graph. One of our results asserts that there are only finitely many finite groups whose SCC-graph has given clique number d, and we find explicitly the list of such groups with d=2. We pose some problems on the relation of the SCC-graph to the solvable graph and to the NCC-graph, which we cannot solve.
Citation
Bhowal , P , Cameron , P J , Nath , R K & Sambale , B 2023 , ' Solvable conjugacy class graph of groups ' , Discrete Mathematics , vol. 346 , no. 8 , 113467 . https://doi.org/10.1016/j.disc.2023.113467
Publication
Discrete Mathematics
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.disc.2023.113467
ISSN
0012-365X
Type
Journal article
Rights
Copyright © 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Description
The fourth author is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1).
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/27454

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