Ray,skew.

This paper discusses the gracefulness of disjoint union of paths such as,proving them graceful when.

文章讨论了形如P2m∪P2m+t的两条路不交并图的优美性,用构造性的方法给出了当t=-1,1,2时的优美标号,并证明它们是优美的。

The gracefulness of disjoint union of paths such as Pm∪P2m+t are discussed.

讨论了形如Pm∪P2m+t的两条路不交并图的优美性,用构造性的方法给出了当t=0,1,2时的优美标号,并证明它们是优美的。

This paper discusses the gracefulness of 3C 4k∪C n which is the disjoint union of four circles, gives out a necessary condition for the 3C 4k∪C n to be a graceful graph, and gives the graceful labelings of 3C 4k∪C 4n+3,3C 4k∪C 4k+4,3C 8k∪C 8k-1.

讨论了 4个圈不交并图 3 C4 k∪ Cn 的优美性 ,给出了其为优美图的必要条件 ,并用构造性的方法给出了 3 C4 k∪ C4 k+3,3 C4 k∪ C4 k+4 ,3 C8k∪ C8k-1的优美标号 ,证明了它们是优美