… in maps is represented by vertex-transitive maps. The simplest examples of such maps are
Cayley maps (the subject of this paper), which are oriented maps whose map automorphism …

… groups of these maps to have nontrivial … the map is a complete graph; a classical theorem
of Frobenius then implies that all vertex-transitive maps are given by our extension of Cayley's …

… Cayley graph can be viewed as a graph which admits a regular group action on its vertices,
a Cayley map is a map … A makes the underlying graph of M a Cayley graph C(A, X). A regular …

… Unlike the exponential map the Cayley map depends on … Cayley map is a continuous map
and I3 is clearly the image of the zero matrix, so we can infer that the image of the Cayley map …

The theorem that four colours are sufficient for any map, is mentioned somewhere by the
late Professor De Morgan, who refers to it as a theorem known to map-makers. To state the …

… M is transitive (and therefore regular), we say that the Cayley map M is a regular Cayley map.
The reader interested in more information on regular maps is advised to consult [1,3] or [9]. …

… , have balanced regular Cayley maps, and that some abelian groups have only unbalanced
regular Cayley maps. In Sections 3 and 4, we consider balanced regular Cayley maps, first …

… For core-free Cayley graphs, we introduce their dual Cayley graphs. This enables … Cayley
maps and circulants graphs, and as well as between regular Cayley maps and dihedral Cayley …

… A Cayley map M is a 2-cell embedding of a Cayley graph in an orientable surface with the
… to regular Cayley maps, and allows for a unified theory of regular Cayley maps and their …

… two types of such maps: the balanced and antibalanced Cayley maps. Part I was devoted
to giving conditions under which a balanced Cayley map is regular or … map automorphism …