$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs

Johnson Awolola defined the $\alpha$-level neutrosophic set in the year 2020. However, this definition is not useful for getting some realistic results. In order to generate more realistic and applicable results, we have introduced a new concept of the $\rho$-level NSs in the form of $\rho$-lower level and $\rho$-upper level sets of a NS. Using several real-world examples, such as choosing personnel for an institutional objective, we discussed our outcomes. Using these examples, we also illustrate the significance of the $\rho$-level NS's, upper and lower boundaries. Along with studying numerous features, we also applied these results to the NG and defined various classes of infinite extendable NGs. Additionally, the theoretical frameworks for infinitely extensible NGs have been developed, with different supporting examples.