化学图的谱及相关性质

项目名称： 化学图的谱及相关性质

项目编号： No.11501486

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 颜娟

作者单位： 新疆大学

项目金额： 18万元

中文摘要： 化学结构可以很简单地表示成图的形式，这样的图也称为化学图，或者分子图。对化学图的研究是图论的重要应用之一。通过对化学图的某些不变量的研究，可以反映相应的化合物的一些物理性质比如沸点、熔点等。目前这个领域的研究主要是针对烷烃类的化合物，即碳氢化合物。化学图中很重要的一种是所谓的六角系统图。这种图是苯环碳氢化合物的图论表示。但是要完全计算出某种六角系统的谱是十分困难的。本项目希望计算一些特殊的化学图的谱，尤其是六角系统图的谱。这些图的谱有助于估计对应的化合物的有关能量等其他方面的物理性质。

中文关键词： 图；化学图；特征多项式；谱

英文摘要： A chemical structure can be conveniently represented by a graph, which is called a chemical graph or a molecular graph. Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena. Graph theory is used to mathematically model molecules in order to gain insight into the physical properties of these chemical compounds. Some physical properties, such as the boiling point, are related to the geometric structure of the compound. This is especially true in the case of chemical compounds known as alkanes. Alkanes are organic compounds exclusively composed of carbon and hydrogen atoms. Hexagonal systems are of great importance for theoretical chemistry because they are the natural graph representation of benzenoid hydrocarbons. A considerable a amount of research in mathematical chemistry has been devoted to hexagonal systems. But it is very difficult to determine the spectra of hexagonal graphs. This project mainly puts emphasis on calculating the spectra of chemical graphs and hexagonal systems. This may help to estimate the physical properties of the chemical compounds.

英文关键词： graph;chemical graph;characteristic polynomial;spectrum