图C4k∪Pn的优美性

Gracefulness of the Graphs C4k∪Pn

研究了圈与路不交并图C4k∪Pn,n≥k+2的优美性.首先利用弱优美性的定义,给出了与所研究问题等价的两个命题,把C4k∪Pn,n≥k+2优美性的证明转化为若干路弱优美性的证明,使问题简单化.接着用这种方法证明了k=2,3,4,5,6,7时C4k∪Pn,n≥k+2的优美性.

The gracefulness of C4k∪Pn,n≥k+2;which are the disjoint union graphs of cycles and pahts is discussed in this paper. With the concept of weak gracefulness,two propositions equivalent to the problem discussed are given, which simplifies the problem with the transition from proving the gracefulness of C4k∪Pn,n≥k+2,doing the weak gracefulness of paths. Using this method, the gracefulness of C4k∪Pn,n≥k+2;for k=2,3,4,5,6,7 is proved.