Magic and antimagic H-decompositions
Magic and antimagic H-decompositions
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DOI：
10.1016/j.disc.2011.11.041
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
N. Inayah;A. Lladó;Jordi Moragas
中科院分区：
文献类型：
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作者：
N. Inayah;A. Lladó;Jordi Moragas
如果存在一个双射f:V(G)∪E(G)→{0,1，…，|V(G)|+|E(G)|−1}，使得分解中H的每个副本的边和顶点的标号之和为常数，那么将图G分解为图H的同态副本就是H-magic。众所周知，完全图不允许n bbb6的k2幻分解。利用sumset划分问题的结果，我们证明了完全图K2m+1可以被任意有m条边的优美树进行t -幻分解。我们讨论了完全二部图、反幻分解和(a,d)-反幻分解的类似问题。
A decomposition of a graph G into isomorphic copies of a graph H is H-magic if there is a bijection f:V(G)∪E(G)→{0,1,…,|V(G)|+|E(G)|−1} such that the sum of labels of edges and vertices of each copy of H in the decomposition is constant. It is known that complete graphs do not admit K2-magic decompositions for n>6. By using the results on the sumset partition problem, we show that the complete graph K2m+1admits T-magic decompositions by any graceful tree with m edges. We address analogous problems for complete bipartite graphs and for antimagic and (a,d)-antimagic decompositions.