Solvable conjugacy class graph of groups

authored by

Parthajit Bhowal, Peter J. Cameron, Rajat Kanti Nath, Benjamin Sambale

Abstract

In this paper we introduce the graph Γ

_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∈C and y∈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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Tezpur University
University of St. Andrews

Type

Article

Journal

Discrete Mathematics

Volume

346

ISSN

0012-365X

Publication date

08.2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Theoretical Computer Science, Discrete Mathematics and Combinatorics

Electronic version(s)

https://doi.org/10.1016/j.disc.2023.113467 (Access: Open)
https://doi.org/10.48550/arXiv.2112.02613 (Access: Open)