Connectivity index of directed rough fuzzy graphs and its application in traffic flow network

The directed rough fuzzy graph (DRFG) is a fusion of and theory, as it deals with incomplete vague information simultaneously. Connection or the strength connectivity $$(\mathcal{S}\mathcal{C})$$ vital in realm circuits networks that are linked to real world. As result, $$\mathcal{S}\mathcal{C} $$ one most essential aspects network system. neighborhood index $$(\mathcal {NCI})$$ such parameter has variety applications theory. In this study, our main objective present new topological $$\mathcal {NCI}$$ based on DRFGs solve complicated problems. Motivated by modeling networks, vertices their neighboring vertices, efficiency complex problems, we aim study NCI DRFGs. paper, successfully introduce notion deal uncertainties arise real-world Based provide several lower upper bounds for reference other invariants number edges, degree distance. When operations large DRFG provides confusing picture. Therefore, mechanism determine therefore required. generalized formulas obtained union, composition, Cartesian product also developed. An algorithm obtaining proposed. Further, an application traffic flow was discussed identify busiest intersection using proposed algorithm. Finally, illustrate comparative analysis table established approach ( ) existing techniques (connectivity $$(\mathcal{C}\mathcal{I})$$ Wiener $$(\mathcal{W}\mathcal{I})$$ shown demonstrate validity presented approach.