Solvable conjugacy class graph of groups

被引:6
作者
Bhowal, Parthajit [1 ,2 ]
Cameron, Peter J. [3 ]
Nath, Rajat Kanti [1 ]
Sambale, Benjamin [4 ]
机构
[1] Tezpur Univ, Dept Math, Sonitpur 784028, Assam, India
[2] Cachar Coll, Dept Math, Silchar 788001, Assam, India
[3] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland
[4] Leibniz Univ Hannover, Inst Algebra Zahlentheorie & Diskrete Math, D-30167 Hannover, Germany
关键词
Graph; Conjugacy class; Non-solvable group; Clique number;
D O I
10.1016/j.disc.2023.113467
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 is an element of C and y is an element of D such that < x, y > is solvable. 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. (c) 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/).
引用
收藏
页数:8
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