Modular product of soft directed graphs

Abstract

Soft set theory was proposed by D. Molodtsov as a mathematical framework for dealing with uncertain data. Many academics are now applying soft set theory in decision-making problems. In graph theory, a directed graph is a graph made up of vertices connected by directed edges, also known as arcs. Using directed graphs, it is possible to examine and find solutions to problems relating to social connections, shortest paths, electrical circuits etc. Soft directed graphs were introduced by applying the concept of soft set to directed graphs. They provide a parameterized point of view for directed graphs. In this work, we introduce the modular product and the restricted modular product of soft directed graphs. We prove that these products are also soft directed graphs and we develop the formulas for determining the vertex count, the arc count and the sum of degrees in them.