In this paper the concept of split domination and non -split domination in bipolar fuzzy graphs are introduced and investigated some of their properties. Also relationship between connected domination, split domination, strong split domination and non -split domination number in bipolar fuzzy graphs are discussed.

In this paper, we introduced equitable edge dominating set, equitable edge domination number of fuzzy graphs and also obtain some bounds for equitable edge domination number. Also give some necessary and sufficient conditions for the equitable edge dominating set. Further introduction to connected equitable edge dominating set, connected equitable edge domination number of fuzzy graphs and their some relations are discussed.

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