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<p>A perfect code <i>C</i> in a graph <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1675_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation> is an independent set of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1675_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation> such that every vertex not in <i>C</i> is adjacent to exactly one vertex in <i>C</i>. A subgroup perfect code in a group <i>G</i> is a subgroup that can be represented as a perfect code in a Cayley graph of <i>G</i>. This paper focuses on maximal subgroups of Lie type simple groups of rank one and determines which one of them is a subgroup perfect code.</p>

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Subgroup perfect codes in lie type simple groups of rank one

  • 期刊论文

  • 发表日期：

    2025年7月3日

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  • Zheng Gao Chen,
  • Jing Jian Li,
  • Jun Yang Zhang

摘要

A perfect code C in a graph \(\Gamma \) Γ is an independent set of \(\Gamma \) Γ such that every vertex not in C is adjacent to exactly one vertex in C. A subgroup perfect code in a group G is a subgroup that can be represented as a perfect code in a Cayley graph of G. This paper focuses on maximal subgroups of Lie type simple groups of rank one and determines which one of them is a subgroup perfect code.