Abstract
In this research article, we introduce the notion of q-rung picture fuzzy graph structures (q-RPFGSs). Further, we present the concepts of $$S_{i}$$ -strongly regular q-RPFGSs and $$S_{i}$$ -uniform q-RPFGSs. We study $$S_{i}$$ -bipartite q-RPFGSs and $$S_{i}$$ -r-partite q-RPFGSs and investigate some useful results of their $$S_{i}$$ -regularity. In addition, we discuss drug trafficking in particular region by using complete 6-partite 15-RPFGS. Moreover, power and economy based dominating relationships of developed countries with rich, progressing and underdeveloped countries are represented by a 4-partite 12-RPFGS. Finally, we describe general procedures of our proposed models by algorithms.
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