论文摘要
Randic在1979年提出了图的解析的概念,它在化学原子图中是一种有效的原子描述.图G的解析是一个二元整数向量（x,y）,其递推定义如下:（1）如果G = K1,那么D（G）=（1,0）.（2）如果G = K2,那么D（G）=（0,1）.（3）如果G足不连通的,那么D（G）=∑ri=1 D（Gi）,这里G1,G2,…,Gr,是G的所有连通分支;如果G是一个阶至少为3的连通图,那么D（G）=∑v∈V （ G ）D （G ?v）.我们用a（G）表示图G的解析D（G）=（x,y）的第一个指标值,b（G）表示其第二个指标值,D（G1）=D（G2）当且仅当a（G1）=a（G2）和6（G1）=b（G2）.图的解析对不同构的图有很高的分辨能力.Randic:等人在2000年提出下而的猜想:设T1,T2为树,则T1≌T2当且仅当D（T1）=D（T2）.此问题至今尚未解决.徐、吴等人最近对图的解析进行了研究,得到了一些基本性质.特别地,他们给出了在阶为n的树中,星K1,n-1有最大的a（T）和b（T）,路Pn有最小的a（T）和b（T）.在引言中介绍了图的解析的背景和一些已有结果.第二章中,我们对单圈图的解析进行了研究.设图△n-3是阶为n的单圈图,它由连接k3的一个顶点和Pn-3的一个端点得到;图K+1,n-1是阶为n的单圈图,由连接K1,n-1中两个度为1的顶点而得到.我们计算了它们的解析值,进而证明了在阶为n≥6的单圈图中,图△n-3有最小的a（G）和b（G）,图k+1,n-1有最大的a（G）和b（G）.在第三章中,我们介绍了图的解析的另一种计算方法,利用此方法得到了完全r部图和图Kn∨K m的解析值,其中图Kn∨K m是通过连接图Kn中每个顶点与图K m中的每个顶点而得到.在第四章中,我们证明了在阶为n≥7的双圈图中,图△*n-6有最小的a（G）和b（G）,其中△*n-6是阶为n的双圈图,由分别连接路Pn-6的两个端点与两个蚝的各一个顶点而得到.
论文目录
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