Graphs Embeddings and Group Actions

A 2-cell embedding of a graph on surface is called a map. The study of maps with high symmetry degree is a lastingly active research topic in topological graph theory, algebraic graph theory, and geometric group theory. This short course will introduce background, literature, current research status, and future research topics about the fantastic area. It will include the contents displayed below.

1. A typical example: Petersen graph on sphere and projective plane.
2. Definition of transitive maps, and 14 types of edge-transitive maps described by Graver-Watkins in Memoirs AMS 126(1997).
3. Symmetrical maps with important families of graphs, including complete graphs, complete bipartite graphs, Hamming graphs, and Johnson graphs.
4. Graphs underlying symmetrical maps and group factorizations.
5. Generators, and coverings of graphs, groups and surfaces.