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In this paper, mixed dominating set, mixed domination number, mixed strong domination number and mixed weak domination number of an M-strong fuzzy graph $G=(\sigma, \mu)$ are defined. Also these numbers are determined for various standard fuzzy graphs. The relationship between these numbers and other well known numbers are derived.

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Abstract:In this paper, effective adjacency matrix of a fuzzy graph is introduced. An algorithm for finding a minimal complementary nil dominating set of fuzzy graph is studied with suitable examples.