【摘要】 将k-优美图的概念进行了推广,引入了k～l 优美图及标号间距的概念,并以此为基础, 分别推出了一般情形下判定非连通图G₁ ∪G₂及G₁ ∪G₂ ∪K₂是优美图的两个充分条件;同时得出了图（C₃ ∨（?）_n）∪St（m）∪K₂是优美图,其中k、l 为自然数,l<k,C₃是长为3的圈,K_n 为n 个顶点的完全图,（?）_n 是K_n 的补图,St（m）表示m+1个顶点的星形树,C₃∨（?）_n 是C₃ 与（?）_n 的联图.更多还原

【Abstract】 The present paper extends the definition of k-graceful graph,presents the two new concepts of k～l GRACEFULL GRAPH and LABELING SPACE.Two sufficient conditions about determining the gracefulness of unconnected graph G₁∪G₂ and G₁∪G₂ ∪K₂ are obtained on the basis of them.In the meanwhile,the graph（C₃∨V （?）_n）∪St（m）∪K₂ is a graceful graph is proved.Where k and l is natural number,l<k,C₃ is 3-cycle,K_n is n-vertex complete graph,（?）_n is the complement of graph K_n,St（m）is（m+1）-vertex star tree,C₃∨（?）_n is the join graph of C₃ and（?）_n.更多还原