【摘要】 本文利用构造法,研究了2类非连通图图m·C3∪Gm-1及m·(P2∨K2—)∪Gm-1的优美性.证明了下面的结论:设m为任意的正整数,Gm-1是表示边数为m-1的优美图,则当m≥2时,图m·C3∪Gm-1及m·(P2∨K2—)∪Gm-1都是优美图.其中,C3是表示三个顶点的回路图,P2∨K2—是两个顶点的路P2与两个孤立顶点的图K2—的联图,m·C3是m个图C3恰有一个公共点的图,m·(P2∨K2—)是m个图P2∨K2—恰有一个公共点的图,G∪Gm-1是把图G与Gm-1不相交并起来所得的非连通图.更多还原

【Abstract】 This paper studies the gracefulness of two non- connected- graphs by using structural approach m·C3∪Gm- 1及 m·( P2∨K2—) ∪Gm- 1. It proves the following conclusions:given m to be an arbitrary positive integer,Gm- 1expresses the graceful graph of edge number as m- 1; when m≥2,the graphs m·C3∪Gm- 1and m·( P2∨K2—) ∪Gm- 1are both graceful graphs. Among them,C3 shows the circuit diagram of three vertexes,P2∨K2—is the join-graph of the path of two vertexes P2 and two isolated vertexes graph K2; m·C3shows that m C3 graphs happen to have a common point graph; m·( P2∨K2—) shows m P2∨K2—graphs happen to own a common point graph; G∪Gm- 1is the non-connected graph by combining the non-intersect graph G and graph Gm- 1.更多还原