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For graph  \(G\) , the first Zagreb index \({M}_{1}\left(G\right)\) and second Zagreb index \({M}_{2}\left(G\right)\) are defined as: \({M}_{1}\left(G\right)={\sum}_{u\in V\left(G\right)}{d}_{G}^{2}\left(u\right)\) and \({M}_{2}\left(G\right)={\sum}_{u\upnu \in E\left(G\right)}{d}_{G}\left(u\right){d}_{G}\left(\upnu \right)\) , where  \({d}_{G}\left(v\right)\)  denotes the degree of vertex  \(v\) in \(G\) . The Hyper-Zagreb index  \(HM\left(G\right)\)  is defined as: \(HM\left(G\right)={\sum}_{u\nu \in E\left(G\right)}{\left[{d}_{G}\left(u\right)+{d}_{G}\left(\nu \right)\right]}^{2}\) . In this paper, we introduce a novel class of F-multiplicity corona graphs and derive explicit formulas for their \({M}_{1}\left(G\right)\) , \({M}_{2}\left(G\right)\) and \(HM\left(G\right)\) . Additionally, we demonstrate the chemical relevance of these graphs through applications in molecular design, highlighting their potential for modeling complex chemical structures.

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Topological Analysis of F-Multiplicity Corona Graphs: Zagreb Indices and Applications in Molecular Design

  • 会议论文

  • 发表日期：

    2025年

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  • Yang Yang,
  • Mengjun Wang,
  • Jiangtao Xu,
  • Jinyun Wang

摘要

For graph  \(G\) , the first Zagreb index \({M}_{1}\left(G\right)\) and second Zagreb index \({M}_{2}\left(G\right)\) are defined as: \({M}_{1}\left(G\right)={\sum}_{u\in V\left(G\right)}{d}_{G}^{2}\left(u\right)\) and \({M}_{2}\left(G\right)={\sum}_{u\upnu \in E\left(G\right)}{d}_{G}\left(u\right){d}_{G}\left(\upnu \right)\) , where  \({d}_{G}\left(v\right)\)  denotes the degree of vertex  \(v\) in \(G\) . The Hyper-Zagreb index  \(HM\left(G\right)\)  is defined as: \(HM\left(G\right)={\sum}_{u\nu \in E\left(G\right)}{\left[{d}_{G}\left(u\right)+{d}_{G}\left(\nu \right)\right]}^{2}\) . In this paper, we introduce a novel class of F-multiplicity corona graphs and derive explicit formulas for their \({M}_{1}\left(G\right)\) , \({M}_{2}\left(G\right)\) and \(HM\left(G\right)\) . Additionally, we demonstrate the chemical relevance of these graphs through applications in molecular design, highlighting their potential for modeling complex chemical structures.