证明了对于正整数k，n，si，ti（si，ti≥2，i=1，2，…，n），图n/U/i=1,Ksi,ti是k-优美图；对于正整数k，d（d≥2），k≠0（roodd）及n，si，ti（si，ti≥2，i=1，2，…，n），图n/U/i=1,Ksi,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].
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