Analytical expressions for topological properties of polycyclic benzenoid networks

Quantitative structure‐activity and structure‐property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure‐based topological indices of these networks enable prediction of chemical properties and the bioactivities of...

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Bibliographic Details
Published in:Journal of chemometrics 2016-11, Vol.30 (11), p.682-697
Main Authors: Arockiaraj, Micheal, Clement, Joseph, Balasubramanian, Krishnan
Format: Article
Language:English
Subjects:
Benzenoids
Biomedical materials
convex polycyclic benzenoid networks
cut method
Exact solutions
Mathematical analysis
Molecular chemistry
Networks
Parallelograms
QSAR of polycyclic aromatics
Surgical implants
topological indices
Topology
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Summary:Quantitative structure‐activity and structure‐property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure‐based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure‐activity and structure‐property relationships methods. We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks. For all such networks, we compute analytical expressions for both vertex‐degree and edge‐based topological indices such as edge‐Wiener, vertex‐edge Wiener, vertex‐Szeged, edge‐Szeged, edge‐vertex Szeged, total‐Szeged, Padmakar‐Ivan, Schultz, Gutman, Randić, generalized Randić, reciprocal Randić, reduced reciprocal Randić, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom‐bond connectivity, harmonic, sum‐connectivity, and geometric‐arithmetic indices. In addition we have obtained expressions for these topological indices for 3 types of parallelogram‐like polycyclic benzenoid networks. Topological indices are designed as basically transforming a molecular graph into a numeric number. In this paper, we have derived the analytical expressions of distance and/or degree‐based topological indices for infinite convex benzenoid networks and three types of parallelogram‐like polycyclic benzenoid networks.
ISSN:0886-9383
1099-128X
DOI:10.1002/cem.2851