Edge connectivity of a neutrosophic graph

Neutosophic graphs are an extension of fuzzy and intuitionistic fuzzy graphs by including the uncertainty, vagueness, and indeterminacy that are normal in the real world. This paper looks into the edge connectivity of a neutrosophic graph, which is a basic parameter that shows how strong and fault-tolerant networks are that are modelled by these graphs. Edge connectivity, which is the smallest number of edges that need to be taken away from a graph to make it trivial or disconnected, is a key concept in figuring out how strong and resilient networks are in many situations. This paper also addresses computational challenges related to determining edge connectivity in neutrosophic graphs. We develop efficient algorithms that minimize computational overhead and ensure accuracy in identifying the critical edge sets. We analyze the performance of these algorithms through both theoretical complexity assessments and empirical evaluations on benchmark datasets. Some of the most important things that the study found were critical edges that, when removed, have a big effect on how connected the graph is and how indeterminacy affects the strength of networks. The research underscores the importance of incorporating neutrosophic parameters into graph connectivity studies to better model and analyse systems characterized by uncertainty and partial knowledge.