Dodecahedron graph arc-transitive regular covering

Graph coverings are a powerful tool for constructing new graphs from small base graph.We get the arc-transitive regular covers of dodecahedral graph with covering transformation group Z_p³ by means of voltage assignment of dodecahedral graph in terms of the technique of coset graph and the representation of simple group A₅ into general linear group GL（3,p）.The technique in this thesis is a new method which was put forward by Du,Kwak and Xu.It is a significant contribution to the research of graph covering with covering transformation group Z_pⁿ,an elementary abelian group.