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arXiv · 2611.05068

Chordality of Enhanced Power Graphs of Finite Simple Groups: A Resolution of a Conjecture

Pallabi Manna
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Abstract

The \emph{enhanced power graph} $\PE(G)$ of a finite group $G$ has vertex set $G$, two elements being adjacent if and only if they generate a cyclic subgroup. We determine the finite simple groups $G$ for which $\PE(G)$ is chordal: they are the cyclic groups of prime order, $\Alt(7)$, $\PSL_2(q)$ ($q\ge4$), $\Sz(q)$ ($q=2^{2n+1}\ge8$) and $\PSL_3(4)$. This answers an open problem of Bubboloni, Fumagalli and Praeger \cite{BFP}. We also prove that for every finite group $G$, if the power graph $P(G)$ is a cograph (resp.\ chordal) then so is $\PE(G)$; the cograph case is a conjecture of Bubboloni, Fumagalli and Praeger \cite{BFP}.

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Pallabi Manna. 2026-11-03. Chordality of Enhanced Power Graphs of Finite Simple Groups: A Resolution of a Conjecture. https://arxiv.org/abs/2611.05068

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