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

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Abstract

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 \(CS(n,\alpha _1)\), \(K_{p_1}\vee (K_{q_1}\cup K_{r_1})\), 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.

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Acknowledgements

The authors would like to express their sincere gratitude to the anonymous referees for valuable suggestions, which led to great deal of improvement of the original manuscript. The UGC of the Government of India is appreciative for the financial assistance for the first author under UGC-Ref. No.: 201610294524 (CSIR-UGC NET NOVEMBER 2020) dated 01/04/2021.

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  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721102, India

    Umapada Jana & Ganesh Ghorai

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  1. Umapada Jana
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  2. Ganesh Ghorai
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Correspondence to Ganesh Ghorai.

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Jana, U., Ghorai, G. On the neighborhood inverse sum indeg index of fuzzy graph with application. J. Appl. Math. Comput. 70, 1211–1239 (2024). https://doi.org/10.1007/s12190-024-02006-6

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