【作者】 李爱民；

【导师】 姜广峰；

【作者基本信息】 北京化工大学 ， 应用数学， 2010， 硕士

【摘要】 碳纳米管和Tutte多项式是近年来受到国际上化学和数学研究者们关注的领域。本文主要利用删除—限制方法来计算一类碳纳米管状图的Tutte多项式。随着碳纳米管状图的横向圈及竖边的增加,其Tutte多项式的计算会变得越来越复杂。为了了解碳纳米管状图的Tutte多项式,分析它们的性质及其特征,我们希望把碳纳米管状图分解为一些基本成分,简化对它的研究。具体的讲,希望知道能否把碳纳米管状图的Tutte多项式分解为若干个基图的Tutte多项式的研究,把对碳纳米管状图的Tutte多项式的研究转化为对基图的Tutte多项式的研究。本文证明了碳纳米管状图的Tutte多项式能用基图的Tutte多项式表示出来,且每一个基图的Tutte多项式也能用相同基图的Tutte多项式表示出来,因此,应用递归的思想在结合Maple程序就解决了该问题。在文章最后部分,我们计算了碳纳米管状图的着色多项式。首先,用Tutte多项式的性质我们得到了碳纳米管状图的着色多项式；其次,我们应用着色多项式的定义,分别对n=0,1,2时对碳纳米管状图的着色多项式进行了计算。更多还原

【Abstract】 Carbon nanotubes and Tutte polynomials of graphs have been paying close attention by chemists and mathematicians respectively. In this thesis, the Tutte polynomials of a special class of tubular graphs, e.g., the carbon nanotube like graphs, are considered.Along with the increasing of the circles and edges of carbon nanotube like graphs, the calculation of Tutte polynomial will become more and more complicated. In order to obtain Tutte polynomials of the special class of carbon nanotube like graphs, we decompose the calculation into calculating Tutte polynomials of several basic graphs, obtained in the process of deletion-restriction. Tutte polynomial can be expressed by those of the basic graphs. Eventually, we obtain a recursive formula of the aimed Tutte polynomial. By Maple package, we can compute Tutte polynomials for all the carbon nanotube like graphs.We also compute the chromatic polynomial of the carbon nanotube like graphs. Firstly, we get the chromatic polynomial through Tutte polynomial. Then, we get the chromatic polynomial of tubular graphs for given n, e.g., n=0,1,2.更多还原