HYPER-CONNECTIVITY INDEX FOR FUZZY GRAPH WITH APPLICATION

HYPER-CONNECTIVITY INDEX FOR FUZZY GRAPH WITH APPLICATION

S. R. Islam, M. Pal

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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 estab- lished 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.

Keywords

Fuzzy graph; Connectivity index; Hyper-connectivity index.