Improved superaugmented eccentric connectivity indices for QSAR/QSPR part I: development and evaluation

Recently reported, new-generation superaugmented eccentric connectivity indices\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {^{SA} \xi^{\text{c}} } \right) $$\end{document} have been significantly improved for the purpose of QSAR/QSPR modeling. Four new superaugmented eccentric connectivity indices (denoted by: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ^{SA} \xi_{4}^{\text{c}} ,\,^{SA} \xi_{5}^{\text{c}} ,\,^{SA} \xi_{6}^{\text{c}} , $$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ^{SA} \xi_{7}^{\text{c}} $$\end{document}) along with their topochemical versions (denoted by: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ^{SAc} \xi_{4}^{\text{c}} ,\,^{SAc} \xi_{5}^{\text{c}} ,\,^{SAc} \xi_{6}^{\text{c}} ,$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ^{SAc} \xi_{7}^{\text{c}} $$\end{document}) have been conceptualized in the present study. The values of these indices for all the possible structure of three, four, and five vertices were computed using an in-house computer program. Proposed topological indices revealed absence of intercorrelation with Wiener’s index (W), Balaban’s index (D), Randic’s molecularconnectivity index (χ), and eccentric connectivity index (ξc). The superaugmented eccentric connectivity index-7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {^{SA} \xi_{7}^{\text{c}} } \right) $$\end{document} exhibited exceptionally high discriminating power of the order of >300,000 for all possible structures containing only five vertices. High sensitivity toward branching, exceptionally high discriminating power amalgamated with negligible degeneracy offer proposed indices a vast potential for use in the characterization of structures, similarity/dissimilarity studies, lead identification, lead optimization, combinatorial library design, and quantitative structure–activity/structure–property relationships to facilitate drug design.