Study on single-valued neutrosophic graph with application in shortest path problem

Fuzzy set and neutrosophic set are two efficient tools to handle the uncertainties and vagueness of any real-world problems. Neutrosophic set is more useful than fuzzy set (intuitionistic fuzzy sets) to manage the uncertainties of a real-life problem. This study introduces some new concepts of single-valued neutrosophic graph (SVNG). The authors have discussed the definition of regular SVNG, complete SVNG and strong SVNG. The shortest path problem is a well-known combinatorial optimisation problem in the field of graph theory due to its various applications. Uncertainty is present in almost every application of shortest path problem which makes it very hard to decide the edge weight properly. The main objective behind the work in this study is to determine an algorithmic technique for shortest path problem which will be very easy and efficient for use in real-life scenarios. In this study, the authors consider neutrosophic number to describe the edge weights of a neutrosophic graph for neutrosophic shortest path problem. An algorithm is introduced to solve this problem. The uncertainties are incorporated in Bellman-Ford algorithm for shortest path problem using neutrosophic number as arc length. They use one numerical example to illustrate the effectiveness of the proposed algorithm.