%0 Journal Article %A Inpoonjai, Ph. %A Jiarasuksakun, T. %T Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations %J Iranian Journal of Mathematical Sciences and Informatics %V 13 %N 2 %U http://ijmsi.ir/article-1-823-en.html %R %D 2018 %K Complete bipartite graphs, Supermagic graphs, Degree-magic graphs, Balanced degree-magic graphs., %X 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 is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+|E(G)|)deg(v)/2. 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. %> http://ijmsi.ir/article-1-823-en.pdf %P 1-13 %& 1 %! %9 Research paper %L A-10-1779-1 %+ Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi %G eng %@ 1735-4463 %[ 2018