en عمومى General پژوهشي Research paper <p>A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G&nbsp;is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)|&nbsp;such that the sum of the labels of the edges incident with any vertex v&nbsp;is equal to (1+|E(G)|)deg(v)/2.&nbsp;Degree-magic graphs extend supermagic regular graphs. In this paper we find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of complete bipartite graphs.</p> Complete bipartite graphs, Supermagic graphs, Degree-magic graphs, Balanced degree-magic graphs. 1 13 http://ijmsi.ir/browse.php?a_code=A-10-1779-1&slc_lang=en&sid=1 Ph. Inpoonjai phaisatcha_in@outlook.com 10031947532846006501 10031947532846006501 Yes Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi T. Jiarasuksakun thiradet.jia@mail.kmutt.ac.th 10031947532846006502 10031947532846006502 No Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi