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<p>For a given graph <i>G</i>, a subset <i>X</i> of <i>E</i>(<i>G</i>) is an edge general position set of <i>G</i> if each three edges of <i>X</i> does not contain a common shortest path. The cardinality of a largest edge general position set of <i>G</i> is called the edge general position number of <i>G</i>, denoted by <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1873_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {gp}_e(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>gp</mtext> <mi>e</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we show a class of graphs with diameter 3 such that their edge general position numbers equal to their size minus 2. In addition, all graphs whose edge general position numbers equal to 4 are characterized.</p>

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The Edge General Position Number of Some Graphs

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Yahan Cao,
  • Shengjin Ji,
  • Lihui Wang

摘要

For a given graph G, a subset X of E(G) is an edge general position set of G if each three edges of X does not contain a common shortest path. The cardinality of a largest edge general position set of G is called the edge general position number of G, denoted by \(\text {gp}_e(G)\) gp e ( G ) . In this paper, we show a class of graphs with diameter 3 such that their edge general position numbers equal to their size minus 2. In addition, all graphs whose edge general position numbers equal to 4 are characterized.