Publication details

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 \(\Gamma_{sc}(G)\) 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 \(\langle x, y\rangle\) 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 \(d=2\).

Organisation(s)
Institute of Algebra, Number Theory and Discrete Mathematics
Type
Preprint
Publication date
05.12.2021
Publication status
E-pub ahead of print
Electronic version(s)
http://arxiv.org/abs/2112.02613v3 (Access: Open)