Hyper-connectivity index for fuzzy graph with application

Abstract

Connectivity concept is one of the most important parameters in fuzzy graphs (FGs). The stability of a FG is dependent on the strength of connectedness between each pair of vertices. Depending on “strength of connectedness between each pair of vertices” hyper-connectivity index for fuzzy graph (FHCI) is introduced and studied this index for various FGs like partial fuzzy subgraph, fuzzy subgraph, complete fuzzy graph, saturated cycle, isomorphic fuzzy graphs, etc. A relation of FHCI is established between fuzzy graph and partial fuzzy subgraph. Also, a relation between FHCI and connectivity index for fuzzy graph (FCI) is provided. In the end of the article, a decision-making problem is presented and solved it by using FHCI. Also, a comparison is provided among related indices on the result of application and shown that our method gives better result.