图C_4∪K_(m,n)的k-优美性及算术性

The k-gracefulness and Arithmetics of Graph C_4∪K_(m,n)

给出了一类非连通图C4∪Km ,n。论证了当k>1 (k∈N)时 ,该图是k优美图 ;当k >[(n - 1 )m +1 ]d +1 (d >1 ;m ,n ,d∈N)时 ,图C4∪Km ,n是 (k ,d)算术图。由此推广了文献 [7]中的一些结论。

This paper has formulated a kind of nonconnected graph C 4∪K m,n ,and proved that the graph C 4∪K m,n is a k graceful graph when k>1(k∈N) ,and that the graph is a ( k,d )arithmetic graph when k>[(n-1)m+1]d+1(d>1 and m,n,d∈N) .Thus,the research has reached some conclusions about reference [7].