关于0-可旋转树

On 0-rotatable trees

  • 摘要: 对于一棵 n 阶树 T, 如果存在一个映射 f : V(T)0,1,2,...,n-1, 使对不同的顶点 x, y V(T), 有f(x)f(y), 且边标号集合f(uv)|uv E(T)=1,2,...,n-1, 其中f(uv)=|f(u)-f(v)|, 那么称 T 为优美树, 并称 f 为 T 的一个优美标号. 进一步, 若对于每一个顶点u V(T), T 总有一个优美标号 f, 使得 f(u) = 0, 则称 T 为 0-可旋转树. 本文构造出无穷多0-可旋转树.

     

    Abstract: For a tree T on n vertices, if it admits a mapping f : V(T)0,1,...,n-1 such that f(x)f(y) for distinct x, y V(T) and an edge uv has its label as f(uv)=|f(u)-f(v)|, and the set f(uv)|uv E(T)=1,2,...,n-1, then we say T is a graceful tree and f a graceful labeling of T. Furthermore, if for any vertex u V(T), T admits a graceful labeling f such that f(u)=0, then we say T to be a 0-rotatable tree. Some constructive methods for building large scale of 0-rotatable trees are given.

     

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