On topological polynomials and indices for metal-organic and cuboctahedral bimetallic networks

Abstract

A molecular graph consists of bonds and atoms, where atoms are present as vertices and bonds are present as edges. We can look at topological invariants and topological polynomials that furnish bioactivity and physio-chemical features for such molecular graphs. These topological invariants, which are usually known as graph invariants, are numerical quantities that relate to the topology of a molecular graph. Let m pq (X) be the number of edges in X such that (ζ a , ζ b ) = (p, q), where ζ a (or ζ b ) present the degree of a (or b). The M-polynomial for X can be determined with the help of relation M ( X ; x , y ) = ∑ p ≤ q m p q ( X ) x p y q M(X;x,y)={\sum }_{p\le q}{m}_{pq}(X){x}^{p}{y}^{q} . In this study, we calculate the M-polynomial, forgotten polynomial, sigma polynomial and Sombor polynomial, and different topological invariants of critical importance, referred to as first, second, modified and augmented Zagreb, inverse and general Randić, harmonic, symmetric division; forgotten and inverse invariants of chemical structures namely metal-organic networks (transition metal-tetra cyano benzene organic network) and cuboctahedral bimetallic networks (MOPs) are retrieved using a generic topological polynomial approach. We also draw the two-dimensional graphical representation of outcomes that express the relationship between topological indices and polynomial structural parameters.

On topological indices and entropies of diamond structure

“…Topological descriptors, which are frequently graph invariants, are numerical numbers that characterize the topology of a chemical graph. A wide range of invariants are explored and applied in theoretical chemistry, pharmaceutical and other fields of science [2,3]. Wiener a chemist in 1947 presented the first topological invariant in order to drive the boiling points of paraffins [4].…”

On Entropy of Some Fractal Structures

“…These descriptors can help estimate the physical and chemical properties of chemical networks. Over the past several decades, numerous topological invariants have been established and studied in chemical literature [38,39], and have been applied to understand various effects of organic materials that depend on their molecular shape. The first topological descriptor was introduced by the chemist Wiener in 1947 to determine the boiling points of paraffin [40].…”