【摘要】 对非连通并图的优美性进行了研究,给出了几类非连通的并图,得出了如下结果:对任意的正整数n,m,设s是不超过n/2的最大整数,Pn是n个顶点的路,St(m)是m+1个顶点的星形树,路P2的补图与路Pn的联图记为An,则当n≥2时,A2n与任意一个具有n-1条边的优美图的并图是一个优美图;当n≥5,m≥s+2时,An与星形树St(m)的并图是一个优美图,从而An与星形树St(n)的并图是一个优美图;当n≥5时,An与任意一条路Pn的并图是一个(n-s)-优美图。更多还原

【Abstract】 To study the gracefulness of unconnected union graphs,several kinds of unconnected union graphs are given and the following results are obtained:for arbitrary positive integer n,m,let s be the greatest integer not greater than n/2,Pn be a path with n vertex,St(m)be a star tree with m+1 vertex,graph An be the join graph of complement of P2 and Pn,then for n≥2,the union of A2n and arbitrary a graceful graph with n-1 edges is a graceful graph;for n≥5,m≥s+2,the union of An and star tree St(m) is a graceful graph,therefore the union of An and star tree St(n) is a graceful grap;for n≥5,the union of An and arbitrary path Pn is a(n-s)-graceful graph.更多还原