Impersonality of the Connectivity Index Recomposition of Topological Indices According to Different Properties

Molecules

Xiao-Ling Peng³  Kai-Tai Fang¹  Qian-Nan Hu² 

[1]Department of Mathematics, Hong Kong Baptist University, Hong Kong, P.R. China

[2]College of Chemistry and Chemical Engineering, Central South University, Changsha, 410083, P.R.China. Tel.: [phone], Fax: [phone]

[3]College of Mathematics, Sichuan University, Chengdu, 610064, P.R. China

关键词: Decomposition;    Recomposition;    topological character bases;    variable connectivity index;   

DOI  :  10.3390/91201089

来源: mdpi

【 摘 要 】

The connectivity index χ can be regarded as the sum of bond contributions. In this article, boiling point (bp)-oriented contributions for each kind of bond are obtained by decomposing the connectivity indices into ten connectivity character bases and then doing a linear regression between bps and the bases. From the comparison of bp-oriented contributions with the contributions assigned by χ, it can be found that they are very similar in percentage, i.e. the relative importance of each particular kind of bond is nearly the same in the two forms of combinations (one is obtained from the regression with boiling point, and the other is decided by the constructor of the χ index). This coincidence shows an impersonality of χ on bond weighting and may provide us another interpretation of the efficiency of the connectivity index on many quantitative structure– activity/property relationship (QSAR or QSPR) results. However, we also found that χ’s weighting formula may not be appropriate for some other properties. In fact, there is no universal weighting formula appropriate for all properties/activities. Recomposition of some topological indices by adjusting the weights upon character bases according to different properties/activities is suggested. This idea of recomposition is applied to the first Zagreb group index M₁ and a large improvement has been achieved.

【 授权许可】

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