本项目所涉及的数学对象包括图，群和曲面；特别地，研究对称图及群在图上和曲面上的作用。近年来，对称图在越来越多的领域里找到了应用：从马尔科夫链混合率，到并行计算中处理器的大型相互作用阵列的通信网络的设计，从基于群论的密码学，到与计算机科学和化学文档相关的图的同构问题。因此，研究传递图对不同领域里的众多重要问题有深刻影响和应用。..本项目计划研究有关对称图的几个重要课题,包括（1）研究边传递图的扩展性质；（2）研究s-弧传递图的正规覆盖；（2）刻画局部s-弧传递图的融合体；（4）刻画黎曼曲面上的边传递地图。其目的是解决有关这些课题的若干个重大问题，在每个课题上取得突破性进展并发展有用的理论，并把得到的结果应用于解决其它领域里的重要问题。

Mathematical objects involved in this project include groups, graphs and surfaces;in particular, it is proposed to study symmetrical graphs and group actions on graphs and surfaces. Increasingly, symmetrical graphs are being used in a wide range of applications: from the mixing rate of Markov chains to the design of interconnection networks for large interacting arrays of processors in parallel computations, from group-based cryptography, to the graph isomorphism problem (of relevence to computer science and to chemical documentation). Studying transitive graphs will therefore significantly impact on many fundamental problems in different areas...This project proposes to study several important topics regarding symmetrical graphs, including (1) investigating expansion property of symmetrical graphs;(2) studying normal covers of s-arc transitive graphs;(3) classifying amalgams of locally s-arc transitive graphs; (4) characerizing edge transitive maps on Riemann surfaces. It aims to solve fundamental problems regarding these topics, and to make significant and breaking progress and to develop useful theory for all of them, and then applying the comes to solve important problems in other areas.