探索金鱼图的奇优美性

A Quest for the Odd-Gracefulness of Goldfish Graph

给出了奇优美图和二分奇优美图的概念,并定义了金鱼图,证明了在鱼头为不同图形的情况下,金鱼图仍然是奇优美的,且是二分奇优美的.还证明了:对一个奇优美图H和一棵二分奇优美树T,用一条边连接T的一个顶点和H的标号基点u_0后所得到的金鱼图仍是奇优美图.

In this paper, two conceptions that odd-graceful graphs and bipartite oddgraceful graphs are mentioned. And defining the goldfish graph, presenting a proof to the odd-gracefulness and the bipartite odd-gracefulness of the goldfish graph even if it has different heads. Moreover, we has been shown that a goldfish graph, while we link a peak of the bipartite odd-graceful tree T and the labeling basic point u0 of H, is odd-graceful.