化学图论是图论与量子化学相互交叉、相互渗透的一门新学科分支，它具有重要的理论意义和应用价值。本项目主要研究图的各种拓扑指数（包括Wiener指数、hyper-Wiener指数、terminal Wiener指数、Harary指数、ABC指数及其各种变形等）的局部函数、可加参数性质及逆问题，建立图的拓扑指数与图的结构（直径、度序列、边数、匹配等图的不变量），图的特征值（图的距离矩阵、邻接矩阵、拉普拉斯矩阵、无符号拉普拉斯矩阵等），特征向量四者之间的关系，研究方法和技巧涉及到图论、量子理论、优超理论、图谱理论等相关领域。预期研究成果将丰富和拓展化学图论的研究领域，一方面为量子化学提供坚实的数学方法和工具，另一方面为图论提供新的课题。

Chemical graph theory is an interwined theory between quantum chemistry and graph theory and plays a key role in theories and applications. With aid of graph theory, quantum theory, majorization theory and spectral graph theory, the project focuses on the local funtions of topological indices (for example, Wiener index, hyper-Wiener index, Harary index and their variants)of graphs and their inverse problems .The main purpose of this project is to establish the relationships among some important topological indices, other invariants (including degree sequence, matching number,diameter etc), the eigenvalues(including distance matrix, adjacent matrix, laplacian matrix and signless laplacian matrix ) of graphs and their corresponding eigenvectors. The expected results will provide rigorous mathematical bases and methods and extend new field of chemical graph theory.