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<p>We investigate independent locating-dominating (ILD) sets in some graph classes constructed from cycles: power of cycles, Möbius ladders, circular ladders, Jahangir graphs, helm graphs and sunflower graphs. These sets are important in applications such as fault detection and monitoring in networks. We demonstrate that power graphs <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44425_2025_23_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_n^k\)</EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44425_2025_23_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(k \geqslant 2\)</EquationSource> </InlineEquation> do not admit ILD sets. For the remaining graph families, we establish exact values for the ILD number and present constructive methods for obtaining minimum ILD sets.</p>

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Independent Locating-Dominating Sets in Some Graphs Constructed from Cycles

  • 期刊论文

  • 发表日期：

    2025年10月8日

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  • Dayllon Vinícius Xavier Lemos,
  • Márcia Rodrigues Cappelle,
  • Erika Morais Martins Coelho,
  • Leslie Richard Foulds,
  • Humberto José Longo

摘要

We investigate independent locating-dominating (ILD) sets in some graph classes constructed from cycles: power of cycles, Möbius ladders, circular ladders, Jahangir graphs, helm graphs and sunflower graphs. These sets are important in applications such as fault detection and monitoring in networks. We demonstrate that power graphs \(C_n^k\) with \(k \geqslant 2\) do not admit ILD sets. For the remaining graph families, we establish exact values for the ILD number and present constructive methods for obtaining minimum ILD sets.