某些种类的优雅龙虾
On certain classes of graceful lobsters
摘要：
一个m边图G=（V，E）是优美的，如果它有一个不同的顶点标号f，一个从V到集合{0，1，2，3，.，m}，其引起不同的边缘标记|f（u）-f（v）|对于E中的边uv。著名的Ringel-Kotzig猜想（1964）是所有的树都是优美的。树T的基是从T中删除其1度顶点得到的。毛毛虫是一棵树，它的底部是一条小路，龙虾是一棵树，它的底部是一条毛毛虫。小路和毛毛虫都是优雅的。接着，Bermond（1979）又指出所有的龙虾都是优雅的。本文利用Bloom（1979）等人提出的邻接矩阵刻画，给出了连接优美图和α-标号图的各种方法。我们应用这些结果得到了一些优雅的龙虾类，并指出如何获得其他一些。
英文摘要：
A graph G=(V,E) with m edges is graceful if it has a distinct vertex labeling f, a map from V into the set{0,1,2,3,...,m} which induces a distinct edge labeling |f(u)-f(v)| for edges uv in E. The famous Ringel-Kotzig conjecture (1964) is that all trees are graceful. The base of a tree T is obtained from T by deleting its one-degree vertices. A caterpillar is a tree whose base is a path and a lobster is a tree whose base is a caterpillar. Paths and caterpillars are known to be graceful. Next it was conjectured by Bermond (1979) that all lobsters are graceful. In this paper we describe various methods of joining graceful graphs and α-labeled graphs using the adjacency matrix characterization that initiated by Bloom (1979) and others. We apply these results to obtain some classes of graceful lobsters and indicate how to obtain some others.
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