Magic and antimagic -decompositions

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• 作者：N. Inayah^a ; ^{innazen@students.itb.ac.id} ; A. Lladó ; ^b ; ^{allado@ma4.upc.edu} ; ^{allado@ma4.upc.es} ; J. Moragas^b ; ^{jmoragas@ma4.upc.edu}
• 关键词：Graph decompositions ; Magic labelings
• 刊名：Discrete Mathematics
• 出版年：2012
• 出版时间：6 April, 2012
• 年：2012
• 卷：312
• 期：7
• 页码：1367-1371
• 全文大小：254 K

文摘

A decomposition of a graph into isomorphic copies of a graph is -magic if there is a bijection such that the sum of labels of edges and vertices of each copy of in the decomposition is constant. It is known that complete graphs do not admit -magic decompositions for . By using the results on the sumset partition problem, we show that the complete graph admits -magic decompositions by any graceful tree with edges. We address analogous problems for complete bipartite graphs and for antimagic and -antimagic decompositions.