Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly
the connections between topological graph theory and other areas of mathematics …

A Cayley map M is a 2-cell embedding of a Cayley graph in an orientable surface with the
same orientation (the induced permutation of generators) at each vertex. The concept of a …

A skew morphism of a finite group 𝐴 is a permutation 𝜑 of 𝐴 fixing the identity element and
for which there is an integer-valued function 𝜋 on 𝐴 such that φ⁢(x⁢ y)= φ⁢(x)⁢ φ π⁢(x)⁢(y) …

Hamilton cycles and paths in vertex-transitive graphs—Current directions - ScienceDirect Skip
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Recently, regular Cayley maps of cyclic groups and dihedral groups have been classified in
[7] and [20], respectively. A nature question is to classify regular Cayley maps of elementary …

The distinguishing number of a group $ A $ acting faithfully on a set $ X $, denoted $ D (A,
X) $, is the least number of colors needed to color the elements of $ X $ so that no …

This paper aims to develop a theory for studying Cayley graphs, especially for those with a
high degree of symmetry. The theory consists of analysing several types of basic Cayley …

A skew-morphism of a finite group G is a permutation σ on G fixing the identity element such
that the product of< σ> with the left regular representation of G forms a permutation group on …

Abstract JE Graver and ME Watkins, Memoirs Am. Math. Soc. 126 (601)(1997) established
that the automorphism group of an edge‐transitive, locally finite map manifests one of …

A skew morphism of a group is a generalisation of an automorphism, arising in the context of
regular Cayley maps or of groups expressible as a product AB of subgroups A and B with B …