Abstract
Picture fuzzy graph (PFG) is a useful tool in fuzzy graph theory that can be used to model a variety of real-world problems involving uncertainty caused by unknown, changing, and indeterminate data. PFG might be more fruitful at solving confusing problems than fuzzy graph (FG) and intuitionistic fuzzy graph (IFG). In this study, some interesting properties and results for the PFGs have been presented by using the concepts of strong arcs. The notions of covering in a PFG, strong node covering, strong arc covering, strong independent set, and matching number have been introduced for PFG. Moreover, we also devised the conception of paired domination, strong paired domination, and strong paired dominating set for a PFG. Furthermore, many interesting properties of these conceptions are established. Additionally, the strong paired domination numbers of complete PFG and complete bipartite PFG have been worked out. In addition, many various intriguing aspects of strong paired domination have been examined.