On the neighborhood inverse sum indeg index of fuzzy graph with application

Using fuzzy graph theoretical and computational methods, the multidisciplinary discipline of chemical graph theory examines the molecular formation of a chemical molecule as a fuzzy graph and looks into related mathematical questions. An effective tool in this field that links a numerical value to a graph formation is the topological index. The neighborhood inverse sum indeg index stands out as a contemporary index derived from neighborhood degree considerations. Neighborhood inverse sum indeg index is a crucial graph metric that is applied in real-world applications like corporate networking and signalling on traffic. So this index is generalized in fuzzy graph. In this paper, the neighborhood inverse sum indeg index is explored for some fuzzy graphs like a tree, double star, subgraph, star, complete fuzzy graph, complete bipartite graph, etc. . We evaluate the effect of neighborhood inverse sum indeg index value when the vertex or edge is deleted from a graph. Moreover, the relationship between two isomorphic fuzzy graphs are determined. We have determined the boundedness of this index for some fuzzy graphs like \(CS(n,\alpha _1)\) $CS(n,{\alpha }_1)$ , \(K_{p_1}\vee (K_{q_1}\cup K_{r_1})\) $K_{p_1}\vee (K_{q_1}\cup K_{r_1})$ , etc. Also a couple of results are found. We all aware that one cause of global warming is the carbon emission. Finally we have found out the country which needs to reduce the carbon emissions by applying the concept of neighborhood inverse sum indeg index.