【摘要】 讨论非连通图(P1∨Pn)∪Gr和(P1∨Pn)∪(P3∨■r)及Wn∪St(m)的优美性,证明了如下结论:设n,m为任意正整数,s=[n/2],r=s-1,Gr是任意具有r条边的优美图,则当n≥4时,非连通图(P1∨Pn)∪Gr和(P1∨Pn)∪(P3∨■r)是优美图;当n≥3,m≥s时,非连通图Wn∪St(m)是优美图.其中,Pn是n个顶点的路,Kn是n个顶点的完全图,K-n是Kn的补图,G1∨G2是图G1与G2的联图,Wn是n+1个顶点的轮图,St(m)是m+1个顶点的星形树.更多还原

【Abstract】 The present paper deals with the gracefulness of three kinds of unconnected graphs(P1∨Pn)∪Gr,(P1∨Pn)∪(P3∨K-r) and Wn∪St(m),and proves the following results: for positive integers n and m,let s=,r=s-1,Gr be a graceful graph with r-edges,if n≥4,then the unconnected graphs(P1∨Pn)∪Gr and(P1∨Pn)∪(P3∨K-r) are both graceful graphs;if n≥3 and m≥s,then the unconnected graph Wn∪St(m) is a graceful graph,where Pn is an n-vertex path,Kn is an n-vertex complete graph,K-n is the complement of graph Kn,graph G1∨G2 is the join graph of G1 and G2,Wn is an(n+1)-vertex wheel graph and St(m) is an(m+1)-vertex star tree.更多还原