Advancements in Soft Directed Graph Theory: New Ideas and Properties

Abstract

The emergence of soft set theory represented a significant advancement in establishing a holistic mathematical framework for handling uncertain data. Currently, numerous scholars are integrating this theory to address decision-making problems. In graph theory, a directed graph consists of vertices connected by directed edges, commonly referred to as arcs. Soft directed graphs are introduced by integrating the principles of soft sets into directed graphs, offering a parameterized perspective on directed graphs. In this paper, we introduce the fundamental notions of order, size, and frequency within the context of soft directed graphs. Furthermore, we establish the concepts of vertex and arc degree sums and explore their properties. Additionally, we delve into the concepts of strong vertex and strong arc, elucidating their significance. Finally, we define the notion of complement within soft directed graphs.