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Topological indices M1/M2 known as first/second Zagreb indices are defined as the sum of the sum/product of degrees of pairs of adjacent vertices of a simple graph. These indices and their properties have been studied in detail under chemical graph theory. In this paper we introduce the concepts of first, second and hyper Zagreb indices of fuzzy graphs. We also study the Zagreb matrices and the associated Zagreb energies of fuzzy graphs. Some bounds for these energies are also obtained.
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