Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 23 min ago
PreprintCC BY 4.0arXiv

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

  • Pallabi Manna
Open at sourcePDFDOICite

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), PSL2(q) (q≥4), Sz(q) (q=22n+1≥8) and PSL3(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}.

Related

  1. An Equivariant Main Conjecture for Branched ℤp-Towers of Finite Graphs and Applications
    Rusiru Gambheera
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. Remarks on the disjoint minimal graphs conjecture
    Allen Weitsman
    arXivPreprintCC0Full textAnalysis & PDEsCombinatorics & discrete mathematicsarXiv
  3. Tuza's Conjecture for Graphs of Maximum Degree at Most 10
    Amrit Kandasamy
    arXivPreprintCC BY-NC-SA 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. Proof of the Göbel-Veldman conjecture on diametrical graphs
    Xingzhi Zhan
    HALPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsHAL
  5. The Borodin--Kostochka Conjecture for Two Classes of Diamond-Free Graphs
    Alireza Fiujlaali
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{manna2026chordality,
  title = {{Chordality of Enhanced Power Graphs of Finite Simple Groups: A Resolution of a Conjecture}},
  author = {Pallabi Manna},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05068},
  eprint = {2611.05068},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05068},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Chordality of Enhanced Power Graphs of Finite Simple Groups: A Resolution of a Conjecture
AU  - Pallabi Manna
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05068
UR  - https://arxiv.org/abs/2611.05068
AB  - 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≥4), Sz(q) (q=2^2n+1≥8) 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}.
ER  -