A study on Single Valued Neutrosophic Graph and its application

Abstract

To deal with the uncertainties and ambiguity of real-world problems, two promising approaches are a fuzzy set and a neutrosophic set.In order to deal with the uncertainties of a real-world scenario, a neutrosophic set is better equipped than a fuzzy set.This study presents a novel single-valued neutrosophic graph (SVNG) idea.Regular, full, and strong SVNG definitions have all been discussed. Along with providing relevant exam- ples, we have also presented many SVNG operations such as rejection, symmetric difference, maximal product, and residue product, as well as some of their key theorems. Then, we have proposed several theorems about the total degree and degree under these operations with some examples. Classical algorithms in graph theory such as Boruvka’s algorithm can only find the minimum spanning tree (MST) in industrial wireless sensor networks. We have described an application of neutrosophic graph in wireless network problem. The classical Boruvka’s algorithm is a well known greedy method for finding the MST of a connected graph.We have modified the classical Boruvka’s algorithm to solve MST problem in neutrosophic enviroment.