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.

Language and culture are allied and interrelated with each other as language carries culture with it while culture depends upon language. The mother language is also one of the most striking elements of any individual's life. At the same time, it also works as an integral tool in the uplift of any nation's future generations. Native language (L1)not only plays the main role in the communication process but also establishes an identity to an individual's entity as well as personality building, a certain class of the masses, and a nation at large. Mother language is a powerful element that engineers the psychological system or structure of an individual to secure the values, norms, history, and trends of a nation. This study has been carried out to focus and discuss the four significant grounds which include the development of a psychological hierarchy of a person with the help of mother tongue, nexuses of culture with mother language, the significance of mother tongue in primary education, and prevailing issues and their relevant solutions. Lastly, it is extracted that the first three elements establish basics and enclose the entire life of a person whereas; the last one nurtures as well as develops one's character, disposition, role, and part to ensure the progress of any nation through the mother tongue.

Topological invariants are the significant invariants that are used to study the physicochemical and thermodynamic characteristics of chemical compounds. Recently, a new bond additive invariant named the Mostar invariant has been introduced. For any connected graph ℋ, the edge Mostar invariant is described as Moe(ℋ)=∑gx∈E(ℋ)|mℋ(g)−mℋ(x)|, where mℋ(g)(or mℋ(x)) is the number of edges of ℋ lying closer to vertex g (or x) than to vertex x (or g). A graph having at most one common vertex between any two cycles is called a cactus graph. In this study, we compute the greatest edge Mostar invariant for cacti graphs with a fixed number of cycles and n vertices. Moreover, we calculate the sharp upper bound of the edge Mostar invariant for cacti graphs in ℭ(n,s), where s is the number of cycles.

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