冠状苯系统的等距离嵌入问题与Wiener指标的计算

兰州大学机构库 >数学与统计学院

	冠状苯系统的等距离嵌入问题与Wiener指标的计算
Alternative Title	An Isometric Embedding Problem of Coronoid Systems and the Calculation of Wiener Index
	徐守军
Thesis Advisor	张和平
	2002-05-12
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	Wiener指标苯系统冠状苯系统
Abstract	Klazvar 等证明了苯系统均可以等距离嵌入到n-方体图Qn 中,从而苯系统是Hamming 图. 本文中我们证明了冠状苯系统(coronoid systems), 即带“洞""的苯系统, 均不能等距离嵌入到n- 方体Q_n 中. 一个图G的Wiener指标是指G中所有顶点对间距离和. Chepoi等在1997 年给出了苯系统Wiener指标的线性算法.在本文中, 我们给出了凸的环状苯系统Wiener 指标的公式; 对于一类较一般的环状苯系统, 通过对其进行变形, 最后变成凸的环状苯系统. 我们给出了每次变形 Wiener指标的改变量,从而也就给出了它的Wiener指标.
Other Abstract	Klavzar et al. showed that any benzenoid system can admit an isometric embedding (alias distance-preserving embedding ) into n-cube Q_n for some n. Here, we show that all coronoid systems (benzenoid systems with “holes"") cannot be iometrically embedded into n-cube Qn. The Wiener index W of a graph is defined as the sum of distances between all pairs of vertices. A formula for W is put forward for any convex primitive coronoid system; Next, we consider a kind of non-convex primitive coronoid systems which can become a convex primitive coronoid system by a series of transformations. By computing the change of Wiener index in each transformation, we obtain a method of computing Wiener index.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/225320
Collection	数学与统计学院
Recommended Citation GB/T 7714	徐守军. 冠状苯系统的等距离嵌入问题与Wiener指标的计算[D]. 兰州. 兰州大学,2002.

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