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<p>Given a finite group <i>G</i> with identity <i>e</i>, the TI-power graph of <i>G</i> is a graph whose vertex set is <i>G</i>, in which distinct <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x,y\in G\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>∈</mo> <mi>G</mi> </mrow> </math></EquationSource> </InlineEquation> are adjacent whenever <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\langle x\rangle \cap \langle y\rangle =\{e\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <mi>x</mi> <mo stretchy="false">⟩</mo> <mo>∩</mo> <mo stretchy="false">⟨</mo> <mi>y</mi> <mo stretchy="false">⟩</mo> <mo>=</mo> <mo stretchy="false">{</mo> <mi>e</mi> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>. This paper classifies all finite groups <i>G</i> whose TI-power graph is planar, toroidal or projective-planar.</p>

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Planar, toroidal and projective-planar TI-power graphs of finite groups

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Xuanlong Ma,
  • Xiaoyan Liu,
  • Guo Zhong

摘要

Given a finite group G with identity e, the TI-power graph of G is a graph whose vertex set is G, in which distinct \(x,y\in G\) x , y ∈ G are adjacent whenever \(\langle x\rangle \cap \langle y\rangle =\{e\}\) ⟨ x ⟩ ∩ ⟨ y ⟩ = { e } . This paper classifies all finite groups G whose TI-power graph is planar, toroidal or projective-planar.