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The non‐F graph of a finite group

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  • Andrea Lucchini
  • Daniele Nemmi

Abstract

Given a formation F, we consider the graph whose vertices are the elements of G and where two vertices g,h∈G are adjacent if and only if g,h∉F. We are interested in the two following questions. Is the set of the isolated vertices of this graph a subgroup of G? Is the subgraph obtained by deleting the isolated vertices a connected graph?

Suggested Citation

  • Andrea Lucchini & Daniele Nemmi, 2021. "The non‐F graph of a finite group," Mathematische Nachrichten, Wiley Blackwell, vol. 294(10), pages 1912-1921, October.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:10:p:1912-1921
    DOI: 10.1002/mana.202000491
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    Cited by:

    1. Gabriela Diaz-Porto & Ismael Gutierrez & Armando Torres-Grandisson, 2022. "The t -Graphs over Finitely Generated Groups and the Minkowski Metric," Mathematics, MDPI, vol. 10(17), pages 1-12, August.

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