Topological measures of molecular graph structure according to degree yield valuable tools that facilitate understanding material’s characteristics through their structures involving physical, chemical, and biological properties. In this study, we have computed the Y-index and Y – polynomial for specific chemical structures, namely V-Phenylenic Nanotube and Nanotorus, as well as their molecular complement graphs. By analyzing the data from the computations using MATLAB, we were able to determine the connection between Y – index and Y – polynomial describing the V-Phenylenic Nanotube and Nanotorus. This elucidation provided insight into the physicochemical properties inherent to these compounds.