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

Abstract

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.