Evaluating the Minimum Spanning Trees Using Prim's Algorithm with Undirected Neutrosophic Graphs

This research paper presents an innovative approach for determining the minimum spanning tree (MST) in an undirected neutrosophic graph using Prim's Algorithm, which is extensively used in addressing network optimization problems. We analyze the effectiveness of Prim's method for constructing the minimum spanning trees in undirected neutrosophic networks, where edge weights are denoted by neutrosophic numbers. Neutrosophic numbers with components reflecting truth, uncertainty, and Neutrosophic Sets and Systems, Vol. 85, 2025 362 Sukanta Ghadei, Amaresh Chandra Panada,Surapati,Pramanik, Nihar Ranjan Panda, Prasanta Kumar Raut, Evaluating the Minimum Spanning Trees Using Prim's Algorithm with Undirected Neutrosophic Graphs falsehood provide a more sophisticated method of expressing uncertainty in network modeling. Here, we use a score function to contrast different NMSTs based on weights calculated by adding neutrosophic numbers. This method is particularly beneficial for use in transportation, communication networks, and logistics, where uncertain properties frequently define network configurations. Numerical illustrations prove the effectiveness of the proposed method, showing its efficiency in handling neutrosophic graphs and keeping it computationally feasible. The results indicated that the suggested Prim's algorithm efficiently produces the minimum spanning trees in uncertain environments and is advantageous for network design and optimization in these scenarios.