Neighborhood Degree Based Topological Indices of Nanotube via Direct and NM‐Polynomial

ABSTRACT The analysis of various chemical structures can be done by using topological indices (TI), graph polynomials, and other useful tools that graph theory offers. The mathematical entries called TI are subtracted from the chemical structure. In this article, we investigate the neighborhood degree based topological indices of TUC4C8(R)$$ TU{C}_4{C}_8(R) $$ nanotube via direct and NM‐polynomial. The indices which we have computed are first, second, third, fourth, fifth NDe indices, third version of Zagreb index, neighborhood second Zagreb index, neighborhood second modified Zagreb index, neighborhood forgotten topological index, neighborhood general Randic index, neighborhood inverse sum index, fourth atom bond connectivity index, fifth geometric arithmetic index, fifth arithmetic geometric index, fifth hyper first and second Zagreb index. Topological indices are numerical descriptors used in mathematical chemistry and chemical graph theory to characterize the topology, or the connectivity pattern, of molecules. These indices provide insights into molecular properties and behaviors without requiring detailed structural information. They are particularly useful in quantitative structure‐activity relationships (QSAR) and molecular modeling studies. In this study we examine different type of topological indices of TUC4C8$$ {\mathrm{TUC}}_4{\mathrm{C}}_8 $$(R) nanotube, is a mathematically alluring item established from squares and octagons. Recent discoveries of numerous types of carbon nanostructures have prompted research into potential applicability in a variety of industries.