Soft Directed Graphs, Their Vertex Degrees, Associated Matrices and Some Product Operations

D. Molodtsov proposed soft set theory in 1999 as a general 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. Electrical circuits, shortest routes, social links and a variety of other problems can all be analyzed and solved using directed graphs. In this paper, we introduce soft directed graphs by applying the concept of soft set to directed graphs. Soft directed graphs provide a parameterized point of view for directed graphs. We define and investigate the degrees and matrices associated with a soft directed graph. We also introduce several product operations in soft directed graphs and analyze some of their features.