非连通图2C_m∪C_n∪P_2的优美性

On the gracefulness of unconnected graph 2C_m∪C_n∪P_2

文章讨论了非连通图2Cm∪Cn∪P2的优美性,证明了如下结论:设k为任意正整数,当m=4k,n=8k,24k,8k-1;m=12k+4,n=8k+3;m=8k+2,n=32k-8,32k+24;m=8k+6,n=40k+20,24k+28时,2Cm∪Cn∪P2都是优美图,当k为任意正整数时(k≥3),非连通图2C4k+2∪C16k+8∪P2是优美图,其中P2是2个顶点的路,Cn是n个顶点的圈。

This paper deals with the gracefulness of unconnected graphs 2Cm ∪ Cn∪ P2 .The following results are proved ：for positive integers k ,if m=4k ,n=8k ,24k ,8k-1 ;m=12k＋4 ,n=8k＋3 ;m=8k＋2 ,n=32k-8 ,32k＋24 ;m=8k＋6 ,n=40k＋20 ,24k＋28 ,the unconnected graphs 2Cm ∪ Cn ∪P2 are graceful graph .For positive integers k（k≥3） ,the unconnected graphs 2C4k＋2 ∪ C16k＋8 ∪ P2 are graceful graph ,w here P2 is a 2-vertex path ,and Cn is a n-vertex cycle graph .