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The notion of the equivalence of vertex labelings on a given graph is introduced. The equivalence of three bimagic labelings for regular graphs is proved. A particular solution is obtained for the problem of the existence of a 1-vertex bimagic vertex labeling of multipartite graphs, namely, for graphs isomorphic with Kn, n, m. It is proved that the sequence of bi-regular graphs Kn(ij) = ((Kn − 1 −...