The problem of lifting graph automorphisms along covering projections and the analysis of
lifted groups is considered in a purely combinatorial setting. The main tools employed …

A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this
paper, the s-regular elementary abelian coverings of the complete bipartite graph K3, 3 and …

A map, that is, a cellular embedding of a graph on a surface, may admit symmetries such as
rotations and reflections. Prominent examples of maps with a 'high level of symmetry7 come …

A k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give
a basic theory of k-orbit maps and classify them up to k⩽ 4.“Hurwitz-like” upper bounds for …

A regular map of type {m, n} is a 2-cell embedding of a graph in an orientable surface, with
the property that for any two directed edges e and e'there exists an orientation-preserving …

Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the
highest possible number of symmetries. The five Platonic solids present the most familar …

A map is a cell decomposition of a closed surface; it is regular if its automorphism group acts
transitively on the flags, mutually incident vertex-edge-face triples. The main purpose of this …

A cellular embedding of a connected graph (also known as a map) on an orientable surface
has trinity symmetry if it is isomorphic to both its dual and its Petrie dual. A map is regular if …

Regular homomorphisms of oriented maps essentially arise from a factorization by a
subgroup of automorphisms. This kind of map homomorphism is studied in detail, and …

A graph is 1-regular if its automorphism group acts regularly on the set of its arcs. Miller [J.
Comb. Theory, B, 10 (1971), 163–182] constructed an infinite family of cubic 1-regular …