两类非连通图优美性的研究

给出了两类非连通图(K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi)和(K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1(k=1,2), 并证明了如下结论:对自然数n, m, m1, m2, m3, 设s=〖JB(［〗〖SX(〗n〖〗2〖SX)〗〖JB)］〗, n≥9, m1≥s+2, 则图(K2〖TX-〗∨Cn)∪[DD(]3[]i=1[DD)]St(mi)是一个优美图; 对 k=1,2,设n, m≥3, G(k)n-1是一个具有n-1条边的k-优美图,则图(K2〖TX-〗∨C2n+k)∪St(m)∪G(k)n-1是一个优美图。 其中,K2是一个具有2个顶点的完全图,K2〖TX-〗是图K2的补图,K2〖TX-〗∨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。

The researches on gracefilness of two kinds of unconnected graphs

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=[n/2], 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.