Soft Directed Graphs, Some of Their Operations, and Properties

Abstract

The soft set theory proposed by D. Molodtsov in 1999 is a general mathematical method for dealing with uncertain data. Now many researchers are applying soft set theory in decision making problems. Graph theory is the mathematical study of objects and their pairwise relationships, known as vertices and edges, respectively. The concept of soft graphs is used to provide a parameterized point of view for graphs. Directed graphs can be used to analyze and resolve problems with electrical circuits, project timelines, shortest routes, social links and many other issues. We introduced the notion of the soft directed graph by applying the concepts of soft set in a directed graph. In this paper, we introduce the concept of soft subdigraph and some soft directed graph operations like AND operation, OR operation, soft union, extended union, extended intersection, restricted union and restricted intersection and investigate some of their properties.