NM-polynomial and neighborhood degree-based indices of 2D-lattice, nanotube, and nanotorus

A topological index is a numerical value derived from the structure of a molecular graph, used to describe its topology and predict chemical, physical, or biological properties. This research investigates neighborhood degree sum-based indices of semi-total (line) graphs derived from 2D-lattice, nanotube, and nanotorus structures represented by $$TUC_4C_8[p,q]$$ . The study computes NM-polynomials for these networks and employs calculus operators to derive various neighborhood degree sum-based indices. Combinatorial computation, graph theoretical techniques, and edge partition methods are utilized to analyze the networks. The results are visualized using Maple 2020, with comparative analysis conducted via 3D line plotting in MATLAB 2017.