Connectivity Index of Directed Rough Fuzzy Graphs and its Application in Traffic Flow Network

Abstract The directed rough fuzzy graph (DRFG) is a fusion of rough and fuzzy theory, because it deals with incomplete and vague information simultaneously. Connection or the strength of connectivity (SC) is vital in the realm of circuits or networks that are linked to the real world. As a result, SC is one of the most essential aspects of a directed rough fuzzy network system. The neighborhood connectivity index (NCI) is one such parameter that has a variety of applications in network theory. In this paper, we discuss the notion of NCI in DRFGs using the strength of vertices to their neighbor vertices. We provide several lower and upper bounds on the NCI of DRFGs with reference to other graph invariants such as the number of vertices, edges, and degree distance. When we study NCI in operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG provides a confusing picture. Therefore, a mechanism to determine the NCI for DRFG operations is needed. Therefore, generalized formulas for NCI of DRFGs obtained by operations such as union, composition, and Cartesian product are also developed. An algorithm for obtaining NCI of DRFGs is also proposed. In addition, an application of NCI of DRFGs in traffic flow networks was discussed to identify the busiest intersection using the proposed algorithm. Finally, we gave a complete comparative evaluation and analysis table for a similar human trafficking system, comparing the results for connectivity index (CI), Wiener index (WI), and NCI.