Abstract
In this manuscript, the theory of constant picture fuzzy graphs (CPFG) is developed. A CPFG is a generalization of constant intuitionistic fuzzy graph (CIFG) and a special case of picture fuzzy graph (PFG). Additionally, the article includes some basic definitions of CPFG such as totally constant picture fuzzy graphs (TCPFGs), constant function, bridge of CPFG, and their related results. Also, an application of CPFG in Wi-Fi network system is discussed. Finally, a comparison of CPFG is established with that of the CIFG which exhibits the superiority of the proposed idea over the existing ones is discussed.