Eccentric connectivity polynomial and Total eccentricity polynomial of \(NA^n_m\) Nanotube

Let \(G\) be a molecular graph with vertex set \(V(G)\) and edge set \(E(G)\). In chemical graph theory, for a molecular graph we have many invariant polynomials and topological indices. The length of a shortest path between two vertices of \(G\) is called distance. In a connected graph \(G\), the eccentricity \(\epsilon(v)\) of vertex \(v\) is the distance between \(v\) and a vertex farthest from \(v\) in \(G\). In this paper, we consider \(NA^n_m\) nanotube and compute eccentric connectivity polynomial and total eccentricity polynomial. Furthermore, we also compute some eccentricity based Zagreb indices of \(NA^n_m\).