Balanced picture fuzzy graph with application

Picture fuzzy graphs are an extension of intuitionistic fuzzy graphs. Balanced picture fuzzy graph is a special type of picture fuzzy graph ( PFG ). In this study, the definition and important properties of PFG like, average PFG , balanced PFG , size, order, density of a PFG , isomorphism, the direct product of two PFG , etc have been studied. The necessary and sufficient conditions for balanced picture fuzzy graphs have also been studied in this article. Beside this, we proposed an algorithm to test whether a PFG is balanced or not. The proof of correctness and an illustration of the proposed algorithm is presented in this article. Lastly, an application of balanced PFG to business alliance is presented.