Abstract
Abstract Several properties of chemical compounds in a molecular structure can be determined with the aid of mathematical languages provided by various types of topological indices. In this paper, we consider eight dendrimer structures in the context of valency based topological indices. We define four Banhatti polynomials for general (molecular) graphs, and compute them for underline dendrimers. We use these polynomials to determine four Banhatti indices. We also determine Zagreb (first, second and hyper) and forgotten indices by developing their relationships with Banhatti indices.
Highlights
The structural formula of molecules and molecular compounds is represented as a molecular graph M in chem- (1) a∈A(M)Combinatorics and chemical graph theory play a significant role to study and characterize molecular structures, spectroscopy, and quantum chemistry [4, 7]
We considered numerous imperative molecular structures and computed their valency based topological indices by defining and computing four Banhatti polynomials
The obtained results are useful in forecasting several molecular properties of chemical compounds such as π−electron energy, medical configuration, boiling point and many more
Summary
The structural formula of molecules and molecular compounds is represented as a molecular graph M in chem- (1) a∈A(M)Combinatorics and chemical graph theory play a significant role to study and characterize molecular structures, spectroscopy, and quantum chemistry [4, 7]. In a newly developed field, called cheminformatics (a combination of chemistry, information and mathematics), qualitative structure activity/property relationships (QSAR) together with topological indices play a vital role for studying molecular compounds with chemical properties of their bioactivities. For such kind of studies, mathematicians and chemists are using several types of topological indices defined on the base of valency of atoms/atombonds, and defined on the base of distance (the number of atom-bonds lying in a shortest path) between atoms of a molecular graph. A topological index is a numerical characterization of a chemical graph and provides a mathematical function of the structure in QSAR studies. There are several valency based topological indices introduced to test the properties of compounds and drugs; such as
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