In this paper we shall show how combinatorial methods can be applied to the study of maps
on orientable surfaces. Our main concern is with maps which possess a certain kind of …

Cayley maps are embeddings of Cayley graphs in orientable surfaces, with the same local
orientation at every vertex. In this paper, conditions will be given under which a Cayley map …

A Cayley map is a Cayley graph embedded in some orientable surface so that the local
rotations at every vertex are identical. In this series we consider two types of such maps: the …

We use the idea (due to Heffter and more recently attributed to Edmonds) of associating with
a map dt on an orientable surface SP a pair of permutations x, y of the set Q. of darts …

A Cayley map is a Cayley graph 2-cell embedded in some orientable surface so that the
local rotations at every vertex are identical. Two types of Cayley maps are introduced: the …

We generalize the idea of reflexibility of a map on a surface by introducing certain integers
as its” exponents “. An exponent is any integer with the property that changing the cyclic …

The aim of this note is to present a short proof of a result of Nedela and Škoviera (J. Graph
Theory19 (1995, 1–11)) concerning those generalized Petersen graphs that are also Cayley …

An orientable map is often presented as a realization of a finite connected graph G in an
orientable surface so that the complementary domains of G, the “faces” of the map are …

In this paper we will define a class of locally non-orientable regular maps called
“cantankerous.” We will show that cantankerous maps are self-Petrie, we will prove a lower …

An orientably-regular map $ M $ is a 2-cell embedding of a connected graph in a closed,
orientable surface, with the property that the group $\mathrm {Aut}^\textrm {o} M $ of all …