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<p>One of the primary objectives in spectral graph theory is to explore how a graph’s structural properties are reflected in the algebraic features of its associated matrices. Among the fundamental tools in this field are the adjacency matrix and graph energy, both of which hold significant theoretical and practical importance. A topological index is a numerical descriptor derived from a molecular graph that captures information about its structure and connectivity, and is commonly used to correlate molecular structure with various physical, chemical, or biological properties. It is considered as numerical molecular descriptor. Degree-based molecular descriptors, in particular, have been extensively studied in the literature. For each such descriptor, a corresponding modified adjacency matrix and an associated graph energy can be defined. This study primarily investigates these extended graph energies based on several well-known degree-based descriptors, emphasizing their usefulness in modeling structure–property relationships through regression analysis.</p>

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Degree-based graph energies as molecular descriptors in QSPR analysis

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Sourav Mondal,
  • Prosanta Sarkar,
  • Zahid Raza

摘要

One of the primary objectives in spectral graph theory is to explore how a graph’s structural properties are reflected in the algebraic features of its associated matrices. Among the fundamental tools in this field are the adjacency matrix and graph energy, both of which hold significant theoretical and practical importance. A topological index is a numerical descriptor derived from a molecular graph that captures information about its structure and connectivity, and is commonly used to correlate molecular structure with various physical, chemical, or biological properties. It is considered as numerical molecular descriptor. Degree-based molecular descriptors, in particular, have been extensively studied in the literature. For each such descriptor, a corresponding modified adjacency matrix and an associated graph energy can be defined. This study primarily investigates these extended graph energies based on several well-known degree-based descriptors, emphasizing their usefulness in modeling structure–property relationships through regression analysis.