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arXiv · 2112.02613

Solvable conjugacy class graph of groups

Parthajit Bhowal·Peter J. Cameron·Rajat Kanti Nath·Benjamin Sambale
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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 $\langle x, y\rangle$ 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 $d=2$.

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BibTeXRIS

Parthajit Bhowal, Peter J. Cameron, Rajat Kanti Nath, Benjamin Sambale. 2021-12-05. Solvable conjugacy class graph of groups. https://arxiv.org/abs/2112.02613

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