传递图是代数图论中一个重要且热门的研究对象，其对称性是由图的自同构群在图上相应元素传递作用来体现的。对称图不仅与数学中代数、几何、拓扑以及组合数学有紧密联系，还在信息科学、编码理论、密码学、生物学、化学、计算机科学等学科有广泛的应用。半对称图是边传递且非点传递的正则图，是传递图中一类重要的图类，此类图的研究具有重要的理论意义和应用价值。本项目将通过图自同构群在图上的作用，以置换群理论和有限群论为主，利用拓扑图论以及组合图论的方法，结合计算机软件辅助来展开研究。本项目旨在丰富半对称图的结果，为置换群在组合结构上的研究提供方法和思路，并探索置换群在代数编码上的应用，同时在研究过程中促进对置换群更深刻的了解。

Transitive graph is an important and active research object in algebraic graph theory, whose symmetry is reflected by the transitive action of the automorphism group on the corresponding elements of the graph. Symmetric graphs are not only closely related to algebra, geometry, topology and combinatorics in mathematics, but also widely used in information science, coding theory, cryptography, biology, chemistry, computer science and so on. The semisymmetric graph is regular, edge-transitive and not vertex-transitive, which is an important family of transitive graphs. The study of such graphs has important theoretical significance and application value. In this project, through the action of automorphism group on the graph, mainly based on permutation group theory and finite group theory, using the methods of topological graph theory and combinatorial graph theory, combined with computer software to carry out the research. This project aims to enrich the results of semisymmetric graphs, provide methods and ideas for permutation groups on combinatorial structures, explore the application on algebraic coding and promote a deeper understanding of permutation groups in the research process.