Abstract
The concept of a neutrosophic set is an extension of a fuzzy set that uses indeterminacy. Similarly, an intuitionistic set has an extension, which is known as a single-valued neutrosophic set. The extension of intuitionistic fuzzy graphs and fuzzy graphs is single-valued neutrosophic fuzzy graphs (SVNF-graphs), which is the new component of graph theory. These versions of graph theory play an important role in many real-world problems, like medical diagnoses, law, engineering, finance, and industry. SVNF-graphs play an important role in linguistics, genetics, networking, sociology, computer technology, economics, and communication. The topological graph parameter gives a real number to the associated graph. There are numerous topological graph parameters proposed in the literature. In topological graph parameters, some uncertainty exists. Rosenfeld, Atanssov, and Smarandache introduced the concepts of a fuzzy graph, intuitionistic fuzzy graph (IFG), and SVNF-graph to overcome these uncertainties. SVNF-graph, IFG, and FG have vital roles in solving world-life problems. In this research work, we proposed a pythonic environment for the single-value neutrosophic fuzzy topological graph parameters. We introduced for the very first time some SVNF-graph parameters, like the Sombor graph parameter: the third and fourth versions of the SVNF-Sombor graph parameters for the SVNF-graph framework. Also, we have proved some characteristics and bounds of these topological graph parameters. We have discussed the social media application for the SVNF-Sombor graph parameter and its third and fourth versions. Under consideration application, We have shown that deleting a person (vertex) in the network can increase or decrease the chances of sending friend requests to other people of artificial intelligence.
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Imran, M., Azeem, M., Jamil, M.K. et al. Exploring innovative single-value neutrosophic fuzzy topological graph parameters. Granul. Comput. 9, 37 (2024). https://doi.org/10.1007/s41066-024-00454-w
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DOI: https://doi.org/10.1007/s41066-024-00454-w