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<p>In graph theory and mathematical chemistry, a topological index is a numerical molecular descriptor that quantifies the structural characteristics of a molecule without considering its three-dimensional structure. The structure-property relationship of chemical compounds can be numerically revealed using topological indices, eliminating the need for wet laboratory testing. Given its strong correlation with molecular properties and activities, the inverse symmetric division degree index (<Emphasis Type="BoldItalic">ISDD</Emphasis>) is a well-established measure. In this work, we begin with mathematical exploration of its exponential variant (<Emphasis Type="BoldItalic">EISDD</Emphasis>). The lower and upper bounds of <Emphasis Type="BoldItalic">EISDD</Emphasis> for various families of graphs, including general connected graphs, trees, and bipartite graphs, are estimated. Corresponding extremal graphs are also examined. Finally, the role of the <Emphasis Type="BoldItalic">EISDD</Emphasis> index in structure-property relationship modelling is analysed. The <Emphasis Type="BoldItalic">EISDD</Emphasis> index is found to model different properties of octanes and some medicinal chemicals with significant accuracy.</p>

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On exponential inverse symmetric division deg index of graphs

  • 期刊论文

  • 发表日期：

    2025年4月28日

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  • Parikshit Das,
  • Sourav Mondal,
  • Zahid Raza,
  • Anita Pal

摘要

In graph theory and mathematical chemistry, a topological index is a numerical molecular descriptor that quantifies the structural characteristics of a molecule without considering its three-dimensional structure. The structure-property relationship of chemical compounds can be numerically revealed using topological indices, eliminating the need for wet laboratory testing. Given its strong correlation with molecular properties and activities, the inverse symmetric division degree index (ISDD) is a well-established measure. In this work, we begin with mathematical exploration of its exponential variant (EISDD). The lower and upper bounds of EISDD for various families of graphs, including general connected graphs, trees, and bipartite graphs, are estimated. Corresponding extremal graphs are also examined. Finally, the role of the EISDD index in structure-property relationship modelling is analysed. The EISDD index is found to model different properties of octanes and some medicinal chemicals with significant accuracy.