On Connectivity of Multidimensional Fuzzy Graphs and its Applications

Connectivity, average connectivity, and its related concepts are prominent notions in fuzzy graph theory that have applications in various areas, including neural networks, transportation problems, cluster analysis, and telecommunication. This work introduces the concepts of connectivity index, average connectivity index, type 2 connectivity index, etc. to a more generalized variant of a fuzzy graph, namely the multidimensional fuzzy graph. Basic results such as the relation of these parameters to vertices and edges, their bounds in some particular multidimensional fuzzy graphs, etc. are studied with proper illustrations. Theorems on the connectivity index of multidimensional fuzzy graphs are obtained after performing operations like direct product, tensor product, composition, join, and so on. Finally, a decision-making problem that can be effectively handled using the connectivity index is demonstrated and compared with others and similar models.