Abstract
V-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate chemical properties of the material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of V-Phylenic nanotubes and nanotori. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.
Highlights
Mathematical models, based on polynomial-representations of chemical compounds, can be used to predict their properties
One well-established method is the computation of a general polynomial whose derivatives or integrals or blend of both, evaluated at some particular point yield topological indices
Hosoya polynomial, is a general polynomial whose derivatives evaluated at 1 produce Weiner and Hyper Weiner indices16
Summary
There are many reasonable arguments about the physical usage of such a simple graph invariant, but the actual fact is still a mystery. First and second Zagreb indices , were introduced by Gutman and Trinajstić defined as: M1(G)=. ∑uv∈E(G)(du + dv) and M2(G) = ∑uv∈E(G)(du × dv) respectively whereas second modified Zagreb index is:. The Symmetric division index which determines surface area of polychlorobiphenyls is defined as:. The other version of Randic index is harmonic index defined as:. This index gives best approximation of heat of formation of alkanes . Let M(G; x, y) = f(x, y) the following Table 1 relates above described topological indices with M-polynomial
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