【摘要】 给出了两类非连通图(K2∨Cn)∪3i=1St(mi)和(K2∨C2n+k)∪St(m)∪G(nk-)1(k=1,2),并证明了如下结论:对自然数n,m,m1,m2,m3,设s=2n,n≥9,m1≥s+2,则图(K2∨Cn)i∪=31St(mi)是一个优美图;对k=1,2,设n,m≥3,G(nk-)1是一个具有n-1条边的k-优美图,则图(K2∨C2n+k)∪St(m)∪G(nk-)1是一个优美图。其中,K2是一个具有2个顶点的完全图,K2是图K2的补图,K2∨Cn是图K2和n圈Cn的联图,St(m)是一个具有m+1个顶点的星形树。更多还原

【Abstract】 Two kinds of unconnected graphs(K2∨Cn)∪3i=1St(mi) and(K2∨C2n+k)∪St(m)∪G(k)n-1(k=1,2) were presented,and following results were proved: for natural number n,m,m1,m2,m3,let s=n2,n≥9,m1≥s+2,then graph(K2∨Cn)∪3i=1St(mi) is a graceful graph;for k=1,2,let n,m≥3,and let G(k)n-1 be a k-graceful graph with n-1 edges,then graph(K2∨C2n+k)∪St(m)∪G(k)n-1 is a graceful graph.Where K2 be a complete graph with 2 vertices,K2 is the complement of graph K2, graph K2∨Cn is the join graph of K2,and n-cycle Cn,St(m) is a star tree with m+1 vertices.更多还原