International Journal For Multidisciplinary Research

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Volume 8 Issue 4
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Topological Indices of Chemical Graphs and Their Applications in QSPR and QSAR Modelling

Author(s) Dr. S NAGARAJAN, Ms. INDU NAIR
Country India
Abstract Chemical graph theory provides an effective mathematical framework for representing molecular structures through graphs, in which atoms are represented by vertices and chemical bonds by edges. Topological indices are numerical invariants of molecular graphs that provide information concerning molecular connectivity, branching, distance, compactness, structural complexity, and other molecular characteristics. The present study investigates selected topological indices and their applications in Quantitative Structure–Property Relationship (QSPR) and Quantitative Structure–Activity Relationship (QSAR) modelling. A dataset consisting of 120 molecular structures was considered. Eight topological indices, namely Wiener index, first Zagreb index, second Zagreb index, Randić index, eccentric connectivity index, graph energy, Kirchhoff index, and Shannon entropy index, were evaluated. Descriptive statistics and correlation analysis were performed, followed by descriptor screening and QSPR and QSAR modelling. The Wiener index showed strong correlations with the Kirchhoff index (r=0.94) and eccentric connectivity index (r=0.91), while the first and second Zagreb indices showed a correlation of (r=0.92). The QSPR model based on the Wiener index, second Zagreb index, and graph energy produced R2=0.892, adjusted R2=0.886, and cross-validated Q2=0.861. The external test-set R2 was 0.861. The QSAR model achieved an accuracy of 88.3% for the training set and 85.0% for the external test set. The findings demonstrate the usefulness of topological descriptors as potential molecular representations and highlight the importance of descriptor selection, validation, and applicability-domain analysis.
Keywords Chemical graph theory, topological indices, Wiener index, Zagreb indices, Randić index, molecular descriptors, QSPR, QSAR, graph invariants, molecular topology
Field Mathematics
Published In Volume 8, Issue 4, July-August 2026
Published On 2026-08-12
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E-ISSN 2582-2160
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CrossRef DOI prefix of IJFMR is 10.36948/ijfmr

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