Automorphism properties of embedded graphs
Joan P. Hutchinson · Journal of Graph Theory · 1984
Abstract This paper presents some conditions under which every automorphism of a graph, embedded on a surface of positive genus, maps face boundaries of the embedding to face boundaries. These results extend a result of Whitney which provides an analogous, but simpler, condition for planar graphs. The new result is applied to graphs on the torus to obtain a classification of many toroidal vertex‐, edge‐, and face‐transitive graphs.