图、多面体与数学化学

Motivated by the molecular structure of fullerenes and nanotubes, we study the structures, classifications and properties of some important type of polytopes and graphs. We also consider the spectral properties of the graphs corresponeding to some molecules and order the graphs by there energy and index. These topics is the inevitable development of matching theory spectra theory and polytope theory. On the other had it can be used to design and.recognize the new materials.

以富勒烯和纳米管等新材料的分子结构为背景，本文研究某些基本而重要的图类和多面体类的构造分类与性质。内容包括双临界图，2-可扩图及其对称性的多面体的构造等公开问题。这本项目还研究图所对应分子的稳定性问题。这问题一方面是图的匹配理论、镨理论及多面体理论的自然发展，一面对预见新材料及其识别具有指导意义。