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<p>Let <i>G</i> be a finite non-abelian group. We associate a commuting graph <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma (G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Γ</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> to <i>G</i>, whose vertices are non-central elements of <i>G</i> and two distinct vertices are adjacent if they commute. In this paper, we characterize all finite non-abelian groups for which the associated commuting graphs have maximum vertex degree at most 5.</p>

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Finite groups with maximum vertex degree commuting graphs

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Qingwei Lian,
  • Jiakuan Lu,
  • Wei Meng

摘要

Let G be a finite non-abelian group. We associate a commuting graph \(\Gamma (G)\) Γ ( G ) to G, whose vertices are non-central elements of G and two distinct vertices are adjacent if they commute. In this paper, we characterize all finite non-abelian groups for which the associated commuting graphs have maximum vertex degree at most 5.