任意n个完备二分图的并图的k-优美性和算术性

The Gracefulness and Arithmetics of the Unions of Arbitrarily n Complete Bipartite Graphs

证明了对于正整数k,n,si,ti(si,ti≥2,i=1,2,…,n),图n∪i=1Ksi,ti是k-优美图;对于正整数k,d(d≥2),k0(mod d)及n,si,ti(si,ti≥2,i=1,2,…,n),图∪ni=1Ksi,ti是(k,d)-算术图.前一结论推广了文[6]的相应结果.

It is proved that the unions of arbitrarily n complete bipartite graphs is a k - graceful graph for any positive integerk ,and that the unions of arbitrarily n complete bipartite graphs is a （k,d）- arithmetic graph for any positive integers k ,d （ d ≥2）, k ≠0（ rood d） . The preceding conclusion generalizes the correspondent results in [6].