Connectivity in Cartesian products of fuzzy graphs: application to decision making

Graph operations on fuzzy graphs aid in understanding the interaction among fuzzy graphs. This article studies connectivity in Cartesian product of fuzzy graphs. The Cartesian product generates a larger and more complex graph, making it difficult to directly assess key connectivity properties such as strength of connectedness, distribution of strong edges, strong degree, fuzzy cutvertices, etc. This study aims to focus on these challenges by deriving the connectivity properties of product graphs from the connectivity features of the component graphs. A characterization of fuzzy bridges in the Cartesian product of fuzzy graphs is obtained. This paper also provides a set of sufficient conditions for identifying fuzzy cutvertices in the Cartesian product. It is observed that the Cartesian product of fuzzy blocks retains the block property. The optimization of transportation of goods between suppliers and warehouses by pinpointing efficient paths in a network is also proposed as an application of this work.