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

Abstract: The connectivity index χ can be regarded as the sum of bond contributions. Inthis article, boiling point (bp)-oriented contributions for each kind of bond are obtainedby decomposing the connectivity indices into ten connectivity character bases and thendoing a linear regression between bps and the bases. From the comparison of bp-orientedcontributions with the contributions assigned by χ, it can be found that they are verysimilar in percentage, i.e. the relative importance of each particular kind of bond is nearlythe same in the two forms of combinations (one is obtained from the regression withboiling point, and the other is decided by the constructor of the χ index). This coincidenceshows an impersonality of χ on bond weighting and may provide us another interpretationof the efficiency of the connectivity index on many quantitative structure–activity/property relationship (QSAR or QSPR) results. However, we also found that χ’sweighting formula may not be appropriate for some other properties. In fact, there is nouniversal weighting formula appropriate for all properties/activities. Recomposition ofsome topological indices by adjusting the weights upon character bases according todifferent properties/activities is suggested. This idea of recomposition is applied to thefirst Zagreb group index M₁ and a large improvement has been achieved.