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.
Results: 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.
Conclusions: 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.