Special irregular neutrosophic graphs

Abstract

Recently, the neutrosophic graph has been introduced as an extension of fuzzy graphs and intuitionistic fuzzy graphs, which offers more compatibility and flexibility than these two types in modeling and structuring many actual issues. In this article, using neutrosophic highly strong arc, the new notions of (totally) special irregular, highly special irregular, strongly special irregular, neighborly special irregular and special arc-irregular of neutrosophic graphs are stated. Finally, one of their utilizations relevant to offering a fixed optimization model in decision making in diverse conditions is presented. In fact,we present a decision-making problem in real-world applied example which discusses the factors influencing a companys efficiency. The presented model is, in fact, a factor-based model wherein the impact score of each factor is divided into two types of direct and indirect influences, in which the concept of neutrosophic special dominating set plays a significant role.