<p>The decomposition of graphs is one of the prominent areas of research in graph theory. The circular ladder graphs are denoted as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1831_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">\(CL_{n}\)</EquationSource> </InlineEquation> and the circular ladder graph can be obtained as <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1831_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="113" /> </InlineMediaObject> <EquationSource Format="TEX">\(CL_{n} = C_{n}\times P_{2}\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1831_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{n}\)</EquationSource> </InlineEquation> is a cycle graph of length <i>n</i> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1831_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(P_{2}\)</EquationSource> </InlineEquation> is a path graph of length one. This paper introduces the edge decomposition of circular ladder graph with 2<i>n</i> vertices and 3<i>n</i> edges. In the main results, a recursive decomposition of the circular ladder graph into claws, cycles, and paths are given.</p>

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Decomposition of Circular Ladder Graph

  • Jhandesh Pegu,
  • Karam Ratan Singh,
  • Laithun Boro,
  • Arun Joram

摘要

The decomposition of graphs is one of the prominent areas of research in graph theory. The circular ladder graphs are denoted as \(CL_{n}\) and the circular ladder graph can be obtained as \(CL_{n} = C_{n}\times P_{2}\) , where \(C_{n}\) is a cycle graph of length n and \(P_{2}\) is a path graph of length one. This paper introduces the edge decomposition of circular ladder graph with 2n vertices and 3n edges. In the main results, a recursive decomposition of the circular ladder graph into claws, cycles, and paths are given.