CAJ | 학술논문

已知树的二分优美标号可以得到一些逼近优美树猜想的结果。给出了树的二分优美标号定义，发现了一类非二分优美树，得到了一些构造大型二分优美树的方法。定义了树的k-二分优美，并且对自然数k6 p2?1证明了任何顶点的优美树都是k-二分优美的。
이지수적이분우미표호가이득도일사핍근우미수시상적결과。급출료수적이분우미표호정의，발현료일류비이분우미수，득도료일사구조대형이분우미수적방법。정의료수적k-이분우미，병차대자연수k6 p2?1증명료임하정점적우미수도시k-이분우미적。
The bipartite labelling of trees was used to produce results that can be regarded as an approximation toward the Graceful Tree Conjecture. The bipartitely graceful labelling of a tree was defined, a class of trees was found to be not bipartitely graceful, and some ways were presented for constructing a large scale of bipartite graceful trees. We defined a k-bipartitely graceful labelling of a tree, and showed that any graceful tree T on p vertices is k-bipartitely graceful with k 6 p2 ?1.