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<p>For a finite group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>, the power graph <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(P(\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is a simple connected graph where the set of vertices consists of the elements of the group <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> and two vertices in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(P(\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are adjacent if and only if one is an integral power of the other. In this paper, we explore the distance spectrum and distance signless Laplacian spectrum of the power graph over a class of split metacyclic groups. We provide lower and upper bounds for the distance spectral radius of the power graph for both the split metacyclic group and the finite cyclic group. Additionally, we establish bounds for the distance signless Laplacian spectral radius of the power graph of a split metacyclic group.</p>

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Distance spectra of power graph over metacyclic group

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Aditya Singh,
  • Yogendra Singh,
  • Anand Kumar Tiwari

摘要

For a finite group \(\Omega \) Ω , the power graph \(P(\Omega )\) P ( Ω ) is a simple connected graph where the set of vertices consists of the elements of the group \(\Omega \) Ω and two vertices in \(P(\Omega )\) P ( Ω ) are adjacent if and only if one is an integral power of the other. In this paper, we explore the distance spectrum and distance signless Laplacian spectrum of the power graph over a class of split metacyclic groups. We provide lower and upper bounds for the distance spectral radius of the power graph for both the split metacyclic group and the finite cyclic group. Additionally, we establish bounds for the distance signless Laplacian spectral radius of the power graph of a split metacyclic group.