Soft Directed Graphs: Exploring Categorical Product

Molodtsov pioneered the soft set theory, offering a mathematical framework tailored for managing uncertain data, a concept now widely embraced by scholars to address decision-making challenges. Directed graphs, comprising nodes connected by directed edges, serve as invaluable tools for analysing and resolving problems related to social connections, optimal routes, electrical circuits, and various other domains. Extending the notion of soft sets to directed graphs, soft directed graphs provide a parameterised approach for understanding relationships within directed graph structures. This study delves into the exploration and analysis of certain characteristics of the categorical and restricted categorical products of soft directed graphs. We establish that these products form soft directed graphs. Detailed results are provided on the node and directed edge counts of both products, along with insights into the directed part in-degree, out-degree, and degree sums of their nodes, enhancing the theoretical foundation of soft directed graphs.