Evaluation of the shortest path by using Bellman-Ford's algorithm in a fermatean neutrosophic environment

The shortest path problem is an extremely important topic in graph theory with numerous real-life applications in science and technology. In this paper, we discuss an improved edition of Bellman-Ford's algorithm for evaluating the shortest path on a connected network with respect to fermatean neutrosophic numbers as the vertex weights of the given network, which is the elongation of a neutrosophic number. It is straightforward to evaluate the shortest path when the environment is certain, but in an uncertain environment, it is difficult, so here we used the fermatean neutrosophic number. Finally, we implemented our suggested methodology with a mathematical example and finally studied a comparative analysis with respect to the dynamic programming approach and with different types of existing algorithms, and discussed the advantages of our methods.