Bonchev D
Department of Marine Sciences, Texas A&M University, Galveston 77551, USA.
J Mol Graph Model. 2001;20(1):65-75. doi: 10.1016/s1093-3263(01)00101-2.
The development of molecular connectivity concept and some of its key elements - Randić's inverse-square-root function and the detailed subgraph characterization - are analyzed. The concept of overall connectivity recently advanced is presented as a next step in unfolding the ideas of molecular connectivity by combining them with those of molecular complexity. Definitions of overall connectivity index, eth-order overall connectivities, and overall connectivity vector are presented along with formulae for calculating these sets of topological indices for several classes of graphs of chemical relevance. Based on sums of adjacencies over all subgraphs (or up to a limiting subgraph size in large molecules), the overall connectivities increase both with molecule size and complexity, as expressed in branching and cyclicity of molecular skeleton. When applied to molecules containing heteroatoms, valence overall connectivities are constructed employing the Kier and Hall scheme. The usefulness of the novel indices is demonstrated by modeling physicochemical properties of alkane compounds. A detailed comparison is made with other models derived for the same set of compounds, proceeding from molecular connectivity, as well as with two other probe connectivity functions--the overall connectivity versions of the second Zagreb index, and a derivative inverse function of this index. The favorable comparisons indicate the need of molecular connectivity paradigm revisiting, and show the potential of the overall connectivity indices for QSPR/QSAR applications.
分析了分子连接性概念的发展及其一些关键要素——兰迪奇的平方根反比函数和详细的子图特征。最近提出的整体连接性概念是将分子连接性概念与分子复杂性概念相结合，从而进一步拓展分子连接性思想的下一步。给出了整体连接性指数、e阶整体连接性和整体连接性向量的定义，以及计算几类具有化学相关性的图的这些拓扑指数集的公式。基于所有子图（或大分子中达到极限子图大小）的邻接和，整体连接性随着分子大小和复杂性的增加而增加，并在分子骨架的分支和环化中得以体现。当应用于含杂原子的分子时，采用基尔和霍尔方案构建价整体连接性。通过对烷烃化合物的物理化学性质进行建模，证明了这些新指数的实用性。与从分子连接性导出的针对同一组化合物的其他模型，以及与另外两个探针连接性函数——第二个 Zagreb 指数的整体连接性版本及其导数反函数进行了详细比较。良好的比较结果表明需要重新审视分子连接性范式，并展示了整体连接性指数在 QSPR/QSAR 应用中的潜力。
