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<p>Topological descriptors are mathematical representations derived from the graph structure of a molecule. Topological descriptors establish a connection between mathematical graph theory and chemical properties, enabling quantitative analysis of molecules. The circumcoronene series is one of the most frequently studied substances in chemical research. Topological indices are categorized according to degree, neighbourhood-degree, distance-based criteria, and polynomial characteristics. In this article, open-neighbourhood-edge-degree-based topological indices are computed for the circumcoronene series of benzenoid (CSB). The following are the topological descriptors obtained : <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(ONE_1(G)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(ONE_2(G)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(ONE_3(G)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(ONE_4(G)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(ONE_5(G)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(ONE_6(G)\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(ONE_7(G)\)</EquationSource> </InlineEquation> for the circumcoronene series. New open-neighbourhood-edge-degree-based indices <i>RONE</i>(<i>G</i>) and <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40009_2025_1866_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="TEX">\(R^*ONE(G)\)</EquationSource> </InlineEquation> are also proposed, calculated for the circumcoronene series of benzenoid. Moreover, an algorithm for computing these indices for a graph has been implemented.</p>

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Computational Analysis of Open-Neighbourhood-Edge-Degree Indices: Algorithmic Evaluation and Graphical Depiction for Circumcoronene Series of Benzenoid Structures

  • 期刊论文

  • 发表日期：

    2025年10月25日

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  • Anbarasan Gayathri,
  • D. Narasimhan

摘要

Topological descriptors are mathematical representations derived from the graph structure of a molecule. Topological descriptors establish a connection between mathematical graph theory and chemical properties, enabling quantitative analysis of molecules. The circumcoronene series is one of the most frequently studied substances in chemical research. Topological indices are categorized according to degree, neighbourhood-degree, distance-based criteria, and polynomial characteristics. In this article, open-neighbourhood-edge-degree-based topological indices are computed for the circumcoronene series of benzenoid (CSB). The following are the topological descriptors obtained : \(ONE_1(G)\) , \(ONE_2(G)\) , \(ONE_3(G)\) , \(ONE_4(G)\) , \(ONE_5(G)\) , \(ONE_6(G)\) , and \(ONE_7(G)\) for the circumcoronene series. New open-neighbourhood-edge-degree-based indices RONE(G) and \(R^*ONE(G)\) are also proposed, calculated for the circumcoronene series of benzenoid. Moreover, an algorithm for computing these indices for a graph has been implemented.