Complexity of chemical graphs in terms of size, branching, and cyclicity

A. T. Balaban; D. Mills; V. Kodali; S. C. Basak

doi:10.1080/10629360600884421

Complexity of chemical graphs in terms of size, branching, and cyclicity

A. T. Balaban, D. Mills, V. Kodali, S. C. Basak

Natural Resources Research Institute

Research output: Contribution to journal › Review article › peer-review

14 Scopus citations

Abstract

Chemical graph complexity depends on many factors, but the main ones are size, branching, and cyclicity. Some molecular descriptors embrace together all these three parameters, which cannot then be disentangled. The topological index J (and its refinements that include accounting for bond multiplicity and the presence of heteroatoms) was designed to compensate in a significant measure for graph size and cyclicity, and therefore it contains information mainly on branching. In order to separate these factors, two new indices (F and G) related with J are proposed, which allow to group together graphs with the same size into families of constitutional formulas differing in their branching and cyclicity. A comparison with other topological indices revealed that a few other topological indices vary similarly with index G, notably DN²S(4) among the triplet indices, and TOTOP among the indices contained in the Molconn-Z program. This comparison involved all possible chemical graphs (i.e. connected planar graphs with vertex degrees not higher than four) with four through six vertices, and all possible alkanes with four through nine carbon atoms.

Original language	English (US)
Pages (from-to)	429-466
Number of pages	38
Journal	SAR and QSAR in environmental research
Volume	17
Issue number	4
DOIs	https://doi.org/10.1080/10629360600884421
State	Published - Aug 1 2006

Bibliographical note

Funding Information:
The help of Dr. Greg Grunwald with the TRIPLET program is gratefully acknowledged. Research reported in this paper was support, in part, by Grant F49620-02-1-0138 from the United States Air Force and Cooperative Agreement Number 572112 from the Agency for Toxic Substances and Disease Registry. This paper represents contribution number 400 from the Center for Water and the Environment of the Natural Resources Research Institute. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.

Keywords

Branching
Centricity
Complexity
Cyclicity
Graph size
New topological indices

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title = "Complexity of chemical graphs in terms of size, branching, and cyclicity",

abstract = "Chemical graph complexity depends on many factors, but the main ones are size, branching, and cyclicity. Some molecular descriptors embrace together all these three parameters, which cannot then be disentangled. The topological index J (and its refinements that include accounting for bond multiplicity and the presence of heteroatoms) was designed to compensate in a significant measure for graph size and cyclicity, and therefore it contains information mainly on branching. In order to separate these factors, two new indices (F and G) related with J are proposed, which allow to group together graphs with the same size into families of constitutional formulas differing in their branching and cyclicity. A comparison with other topological indices revealed that a few other topological indices vary similarly with index G, notably DN2S(4) among the triplet indices, and TOTOP among the indices contained in the Molconn-Z program. This comparison involved all possible chemical graphs (i.e. connected planar graphs with vertex degrees not higher than four) with four through six vertices, and all possible alkanes with four through nine carbon atoms.",

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note = "Funding Information: The help of Dr. Greg Grunwald with the TRIPLET program is gratefully acknowledged. Research reported in this paper was support, in part, by Grant F49620-02-1-0138 from the United States Air Force and Cooperative Agreement Number 572112 from the Agency for Toxic Substances and Disease Registry. This paper represents contribution number 400 from the Center for Water and the Environment of the Natural Resources Research Institute. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.",

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N2 - Chemical graph complexity depends on many factors, but the main ones are size, branching, and cyclicity. Some molecular descriptors embrace together all these three parameters, which cannot then be disentangled. The topological index J (and its refinements that include accounting for bond multiplicity and the presence of heteroatoms) was designed to compensate in a significant measure for graph size and cyclicity, and therefore it contains information mainly on branching. In order to separate these factors, two new indices (F and G) related with J are proposed, which allow to group together graphs with the same size into families of constitutional formulas differing in their branching and cyclicity. A comparison with other topological indices revealed that a few other topological indices vary similarly with index G, notably DN2S(4) among the triplet indices, and TOTOP among the indices contained in the Molconn-Z program. This comparison involved all possible chemical graphs (i.e. connected planar graphs with vertex degrees not higher than four) with four through six vertices, and all possible alkanes with four through nine carbon atoms.

AB - Chemical graph complexity depends on many factors, but the main ones are size, branching, and cyclicity. Some molecular descriptors embrace together all these three parameters, which cannot then be disentangled. The topological index J (and its refinements that include accounting for bond multiplicity and the presence of heteroatoms) was designed to compensate in a significant measure for graph size and cyclicity, and therefore it contains information mainly on branching. In order to separate these factors, two new indices (F and G) related with J are proposed, which allow to group together graphs with the same size into families of constitutional formulas differing in their branching and cyclicity. A comparison with other topological indices revealed that a few other topological indices vary similarly with index G, notably DN2S(4) among the triplet indices, and TOTOP among the indices contained in the Molconn-Z program. This comparison involved all possible chemical graphs (i.e. connected planar graphs with vertex degrees not higher than four) with four through six vertices, and all possible alkanes with four through nine carbon atoms.

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KW - Centricity

KW - Complexity

KW - Cyclicity

KW - Graph size

KW - New topological indices

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Complexity of chemical graphs in terms of size, branching, and cyclicity

Abstract

Bibliographical note

Keywords

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