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

The connectivity index Ç 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...

Full description

Bibliographic Details
Main Authors: Yi-Zeng Liang, Qian-Nan Hu, Kai-Tai Fang, Xiao-Ling Peng
Format: Article
Language:English
Published: MDPI AG 2004-12-01
Series:Molecules
Subjects:
Online Access:http://www.mdpi.com/1420-3049/9/12/1089/
_version_ 1818251211758895104
author Yi-Zeng Liang
Qian-Nan Hu
Kai-Tai Fang
Xiao-Ling Peng
author_facet Yi-Zeng Liang
Qian-Nan Hu
Kai-Tai Fang
Xiao-Ling Peng
author_sort Yi-Zeng Liang
collection DOAJ
description The connectivity index Ç 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 Ç, 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 Ç index). This coincidenceshows an impersonality of Ç 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 Ç’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.
first_indexed 2024-12-12T16:04:41Z
format Article
id doaj.art-3a05dd31515c4bb096bdbcba29541e53
institution Directory Open Access Journal
issn 1420-3049
language English
last_indexed 2024-12-12T16:04:41Z
publishDate 2004-12-01
publisher MDPI AG
record_format Article
series Molecules
spelling doaj.art-3a05dd31515c4bb096bdbcba29541e532022-12-22T00:19:20ZengMDPI AGMolecules1420-30492004-12-019121089109910.3390/91201089Impersonality of the Connectivity Index and Recomposition of Topological Indices According to Different PropertiesYi-Zeng LiangQian-Nan HuKai-Tai FangXiao-Ling PengThe connectivity index Ç 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 Ç, 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 Ç index). This coincidenceshows an impersonality of Ç 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 Ç’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.http://www.mdpi.com/1420-3049/9/12/1089/DecompositionRecompositiontopological character basesvariable connectivity index.
spellingShingle Yi-Zeng Liang
Qian-Nan Hu
Kai-Tai Fang
Xiao-Ling Peng
Impersonality of the Connectivity Index and Recomposition of Topological Indices According to Different Properties
Molecules
Decomposition
Recomposition
topological character bases
variable connectivity index.
title Impersonality of the Connectivity Index and Recomposition of Topological Indices According to Different Properties
title_full Impersonality of the Connectivity Index and Recomposition of Topological Indices According to Different Properties
title_fullStr Impersonality of the Connectivity Index and Recomposition of Topological Indices According to Different Properties
title_full_unstemmed Impersonality of the Connectivity Index and Recomposition of Topological Indices According to Different Properties
title_short Impersonality of the Connectivity Index and Recomposition of Topological Indices According to Different Properties
title_sort impersonality of the connectivity index and recomposition of topological indices according to different properties
topic Decomposition
Recomposition
topological character bases
variable connectivity index.
url http://www.mdpi.com/1420-3049/9/12/1089/
work_keys_str_mv AT yizengliang impersonalityoftheconnectivityindexandrecompositionoftopologicalindicesaccordingtodifferentproperties
AT qiannanhu impersonalityoftheconnectivityindexandrecompositionoftopologicalindicesaccordingtodifferentproperties
AT kaitaifang impersonalityoftheconnectivityindexandrecompositionoftopologicalindicesaccordingtodifferentproperties
AT xiaolingpeng impersonalityoftheconnectivityindexandrecompositionoftopologicalindicesaccordingtodifferentproperties