图_n^2的奇优美及其奇强协调性

Odd gracefulness and odd strongly harmoniousness of the graphs _n^2

该文定义了图_n^2,并研究了该图的奇优美和奇强协调性.利用构造法分别给出了图_n^2在n=4k(k≥2)、n=4k+2时的奇优美算法,在n=4k(k≥2)时,的奇强协调算法,进而证明了图_n^2在n=2k(k≥3)时是奇优美图,在n=4k(k≥2)时是奇强协调图等结论,从而推动了对图的奇优美性和奇强协调性的研究.最后提出猜想:当n=4k+2时,图_n^2不是奇强协调图.

The paper defines C2n and analyzes odd-graceful and odd-strongly harmonious graphs. With the help of construction method, the graphs C2are respectively given when n = 4k（k ≥ 2）、 n =4k ＋ 2 using Oddgraceful Algorithm and when n -= 4k（k 〉 2）using Odd-strongly harmonious Algorithm, and finally it concludes that graph C2n is Odd-graceful graph when n = 2k（k ≥ 3）and are graph Cn2nis Odd-strongly harmonious graph when n = 4k（k≥ 2）,which promotes the study of odd-graceful and odd-strongly harmonious attributes of the graph. The paper also proposes a conjecture that C2n is not a Odd-strongly harmonious graph when n = 4k＋ 2.