Several Types Of The Graceful Graph

The study of graceful geaph began in the1960s A.R osa a paper and G.R ingel a guess, it caused the wide attention of both at home and abroad are put forward. Figure graceful labelling research has extensive applicability, So far have involved subjects with radio astronomy, radar, such as X-ray crystallography. So the figure of the graceful labelling theory has great application value.This article is through the graceful of eulerian graph and Bodeniek guess the solution of the premise and graceful tree conjecture expand research on the issue. Focuses on the following two aspects to study.First, in the graceful of eulerian graph and Bodeniek guess issue studied by constructing circle diagram plus two disjoint string figure graceful, and proved by four kinds of situation. The promotion of a new type of graph (C3+CN)·(Pl+Pm)(N=3,4,6,8,…,2k), and gives its graceful labeling.Second, in the graceful tree problem by constructing under the basis of the three kinds of new trees, respectively, with mark T1,3k5k, T2k,4k2and7said, T1,3k,5k and Tk1(?)k we prove that they are not only graceful tree and alternating graphs, and gives the graceful label and alternating label.For tree Tk1(?)k2studied its graceful and two sets of graceful label is given, secondly Tk Tk1(?)k3·Pm is proved that graceful figure and the tree Tk1(?)k3with the caterpillar adhesive is also a beautiful figure.