2类非连通图的优美性

The Gracefulness of Two Non-connected-graphs

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.

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