Regular maps on non-orientable surfaces
A map on a non-orientable surface is a 2-cell imbedding of a connected graph into the surface; the map is regular if its automorphism group has the largest possible order: four times the number of edges of the graph. It is well-known (see, for example, \textit{H. S. M. Coxeter} and \textit{W. O. J. Moser}, Generators and relations for discrete groups, 4th edition, Springer-Verlag, Berlin (1980; Zbl 0422.20001)) that there are regular maps on the projective plane \(N_1\) (the two-fold covering projection of the dodecahedron imbeds the Petersen graph regularly on the projective plane, for example), but there are no regular maps either on the Klein bottle \(N_2\) or on \(N_3\). The present authors construct several infinite families of regular maps, to show that such maps exist on non- orientable surfaces of more than 77\% of all possible genera.
scientific article; zbMATH DE number 806257
scientific article