Inverse Fuzzy-Directed Graph With an Application in Traffic Flow Problem - R. Keerthana; S. Venkatesh; R. U. Gobithaasan; Jamal Salah (Journal of Mathematics)
The fuzzy-directed graph is an efficient tool to deal with the directional relationships among the nodes that possess imprecise and uncertain information. To handle the membership value of the edges that provide greater effect when two nodes are combined, we introduce inverse fuzzy-directed graph (IFDG) GDI. In this article, we introduce various types of subgraphs of IFDG, the degree of IFDG, and the underlying graph of IFDG. In addition, various IFDG operations, quasidirected union, quasidirected cartesian product, and converse of IFDG are defined and discussed in detail. Furthermore, the notion of isomorphism is defined for GDI. Vertex connectedness of IFDG and its various forms, strongly connected, partially semiconnected, and weakly connected are introduced for GDI and their related results are discussed briefly. Also, the necessary and sufficient conditions for strongly connected, partially semiconnected, and weakly connected IFDGS have been proven. The concluding segment demonstrates the practicality of employing the IFDG algorithm to identify the most congested traffic flows in Kumbakonam, Tamil Nadu, India.