一类新的优美图的构造及其证明

摘要

Graceful graph is one of the most interesting and important research topics in graph theory with wide application and research prospects. We have proposed a new type of graceful composing method and proved that they are all graceful graphs with strict mathematical proof in this paper, as a result, we obtained the conclusion that Gn = T V kn are all graceful graphs with labeling algorithm and so on. Our new graceful labeling is different from the existed results in the literature.%优美图是图论中极为有趣的重要研究课题之一，有着广泛的应用价值和研究前景．讨论了一类新的构造优美图的方法，并且给出了它们都是优美图的严格的数学证明，从而得到了图Gn=TVkn具有优美标号算法并且都是优美图等结论．所给的新的优美标号不同于现有的文献的结果．