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# Solvable conjugacy class graph of groups

verfasst von
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 $d=2$.

Organisationseinheit(en)
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Typ
Preprint
Publikationsdatum
05.12.2021
Publikationsstatus
Elektronisch veröffentlicht (E-Pub)
Elektronische Version(en)
http://arxiv.org/abs/2112.02613v3 (Zugang: Offen)