On neighborhood inverse sum indeg index of molecular graphs with chemical significance

Chemical graph theory is an interdisciplinary field that analyses the molecular structure of a chemical compound as a graph and investigates related mathematical queries by employing graph theoretical and computational techniques. The topological index is an important tool in this area that associates a numerical value with a graph structure. It can be interpreted as a real-valued function that represents the physico-chemical information of a chemical compound. One of the most recently reported neighbourhood degree sum-based indices is the neighbourhood inverse sum indeg index (NI). In this work, we first investigate the application potential of the NI index by exploring its predictive potential and isomer discrimination ability. Following that, some fascinating mathematical features of NI are revealed. Extremal values of NI are estimated for the class of all trees and unicyclic graphs. Furthermore, some crucial upper bounds on NI are set up in terms of well-known graph parameters, including graph order,independence number, and vertex connectivity. Associations between NI and existing indices are also demonstrated.