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<p>Let <i>G</i> be a connected graph and let <i>X</i> be a subset of <i>E</i>(<i>G</i>). Then <i>X</i> is an edge general position set if as soon as <i>P</i> is a shortest (<i>u</i>,&#xa0;<i>v</i>)-path of <i>G</i>, we have <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1870_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="117" /> </InlineMediaObject> <EquationSource Format="TEX">\(|E(P)\cap X|\le 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mi>P</mi> <mo stretchy="false">)</mo> <mo>∩</mo> <mi>X</mi> <mo stretchy="false">|</mo> <mo>≤</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. The cardinality of a largest edge general position set of <i>G</i> is denoted by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1870_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{gp}_\textrm{e}(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>gp</mtext> <mtext>e</mtext> </msub> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and called the edge general position number of <i>G</i>. In this paper, the edge general position number 4 is completely characterized for general graphs.</p>

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Graphs Whose Edge General Position Number is 4

  • 期刊论文

  • 发表日期：

    2025年4月16日

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  • Zhuo-Long Li,
  • Shi-Cai Gong

摘要

Let G be a connected graph and let X be a subset of E(G). Then X is an edge general position set if as soon as P is a shortest (u, v)-path of G, we have \(|E(P)\cap X|\le 2\) | E ( P ) ∩ X | ≤ 2 . The cardinality of a largest edge general position set of G is denoted by \(\textrm{gp}_\textrm{e}(G)\) gp e ( G ) and called the edge general position number of G. In this paper, the edge general position number 4 is completely characterized for general graphs.