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<p>The distance energy of a simple undirected graph <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="236_2025_491_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation>, denoted by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="236_2025_491_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {E}_D(\mathcal {G})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">E</mi> <mi>D</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, is the sum of the absolute values of the eigenvalues of the distance matrix <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="236_2025_491_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(D(\mathcal {G})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>D</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="236_2025_491_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation>. In this paper, we study the effects on distance energy of some special complete <i>t</i>-partite graphs due to embedding an edge. This paper is motivated by the study in a 2022 paper by Wang and Meng.</p>

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Effects on distance energy of some special complete multipartite graphs by embedding an edge

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Masood Ur Rehman,
  • Muhammad Ajmal

摘要

The distance energy of a simple undirected graph \(\mathcal {G}\) G , denoted by \(\mathcal {E}_D(\mathcal {G})\) E D ( G ) , is the sum of the absolute values of the eigenvalues of the distance matrix \(D(\mathcal {G})\) D ( G ) of \(\mathcal {G}\) G . In this paper, we study the effects on distance energy of some special complete t-partite graphs due to embedding an edge. This paper is motivated by the study in a 2022 paper by Wang and Meng.