On Graph theoretic index of Complementary Benzenoids And Macromolecules

Abstract

A topological index of a graph G is a numerical parameter related to G which characterizes its molecular topology. In the field of QSAR and QSPR research, theoretical properties of the chemical compounds and their molecular topological indices such as distance connectivity indices and degree connectivity indices are used to predict the bioactivity of different molecular compounds. Such an approach is different from the traditional QSAR methodology, where one employs selected simpler physico-chemical properties to predict biological activities of molecules. In order to obtain the structure-activity relationships in which theoretical and computational methods are necessary to find appropriate representations of the molecular structure of chemical compounds. These representations are realized through the molecular descriptors. Molecular descriptors are numbers containing structural information derived from the structural representation used for molecules under study. A topological index defined on molecular structure G can be considered as a real valued function f :G→ R+ which maps each durg molecular structure to certain real numbers. Graphene sheets are composed of carbon atoms linked in hexagonal shapes with each carbon atom covalently bonded to three other carbon atoms. Each sheet of graphene is only one atom thick and each graphene sheet is considered a single molecule. Graphene has the same structure of carbon atoms linked in hexagonal shapes to form carbon nanotubes, but graphene is flat rather than cylindrical.. This paper addresses the problem of computing the Wiener , First Zagreb index and Forgotten index of Complementary graphs of graphene sheets, triangular benzenoid graph, circumcoronene molecular graph and nanostar dendrimers. The line graphs were used for modeling amino acid sequences of proteins and of the genetic code. The connected graphs are isomorphic to self complementary graphs. Recently, molecular graphs have proved to be highly useful for drugs activity. Non empirical parameters of chemical structures derived from graph theoretic formalisms are being widely used by many researchers in studies pertaining to molecular design, pharmaceutical drug-design, and environmental hazard assessment of chemicals.