【摘要】 给出了非连通图(K1∨(P(1)n∪P(2)n))∪P(3)n和(K1∨(P(1)n∪P(2)n))∪St(n),且对其优美性进行了研究。证明了如下结论:设n为任意正整数,则当n≥4时,非连通图(K1∨(P(1)n∪P(2)n))∪P(3)n和(K1∨(P(1)n∪P(2)n))∪St(n)均是优美图;其中,Pn是n个顶点的路,Kn是n个顶点的完全图,St(n)是n+1个顶点的星形树,G1∨G2是图G1与G2的联图。更多还原

【Abstract】 The unconnected graphs(K1∨(P(1) n∪P(2) n))∪P(3) n,and(K1∨(P(1) n∪P(2) n))∪St(n) are presented,and their gracefulness is studied. It is proved that for positive integer n,if n≥4 then the unconnected graphs(K1∨(P(1) n∪P(2) n))∪P(3) n,and(K1∨(P(1) n∪P(2) n))∪St(n) are graceful graphs; if n≥3 and m≥s then unconnected graph Wn∪St(m) is a graceful graph; in the meanwhile. Where Pnis n-vertex path,Knis n-vertex complete graph,St(n) is( n + 1)-vertex star tree,graph G1∨G2is the join graph of G1and G2.更多还原