Graceful labellings of paths
Graceful labellings of paths
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优雅的路径标签
DOI：
10.1016/j.disc.2007.03.046
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Rohan Cattell
中科院分区：
文献类型：
--
作者：
Rohan Cattell
简单地证明了每条路都有一个优美的标号，而本文证明了给定几乎任何有n个顶点的路P，则对每个顶点v∈V(P)和对每个整数i∈{0，…，n-1}存在P的一个优美标号，使得v有标号i。我们精确地证明了这些标号何时也可以是α-标号。然后，我们将这一结果推广到强边魔术标号。在得到这些结果时，我们大量使用了π-标号的α-表示，并回顾了Kotzig和Rosa的一些相关结果。
It is easily shown that every path has a graceful labelling, however, in this paper we show that given almost any path P with n vertices then for every vertex v∈V(P) and for every integer i∈{0,…,n-1} there is a graceful labelling of P such that v has label i. We show precisely when these labellings can also be α-labellings. We then extend this result to strong edge-magic labellings. In obtaining these results we make heavy use of π-representations of α-labellings and review some relevant results of Kotzig and Rosa.