Cayley maps

Authors:
R. Bruce Richter;Jozef Širáň;Robert Jajcay;Thomas W. Tucker;Mark E. Watkins
Affiliations:
University of Waterloo, Waterloo, Canada;Slovak University of Technology, Bratislava, Slovakia;Indiana State University, Terre Haute, IN;Colgate University, Hamilton, NY;Syracuse University, Syracuse, NY
Venue:
Journal of Combinatorial Theory Series B
Year:
2005

Citing 12
Cited 12

Tilings and patterns

Tilings and patterns
Topological graph theory

Topological graph theory
Regular maps from Cayley graphs, part 1: balanced Cayley maps

Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Automorphism groups of Cayley maps

Journal of Combinatorial Theory Series B
Regular maps from Cayley graphs II: antibalanced Cayley maps

Proceedings of the first Malta conference on Graphs and combinatorics
On a new product of groups

European Journal of Combinatorics
Vertex-transitive graphs that are not Cayley graphs. II

Journal of Graph Theory
Automorphism groups and isomorphisms of Cayley digraphs

Discrete Mathematics - Special issue on Graph theory
Self-dual Cayley maps

European Journal of Combinatorics
The Structure of Automorphism Groups of Cayley Graphs and Maps

Journal of Algebraic Combinatorics: An International Journal
On the number of nonisomorphic orientable regular embeddings of complete graphs

Journal of Combinatorial Theory Series B
Skew-morphisms of regular Cayley maps

Discrete Mathematics - Algebraic and topological methods in graph theory

Regular t-balanced Cayley maps

Journal of Combinatorial Theory Series B
Regular Cayley maps for finite abelian groups

Journal of Algebraic Combinatorics: An International Journal
F-actions and parallel-product decomposition of reflexible maps

Journal of Algebraic Combinatorics: An International Journal
On 2-fold covers of graphs

Journal of Combinatorial Theory Series B
A classification of regular t-balanced Cayley maps on dicyclic groups

European Journal of Combinatorics
Reflexibility of regular Cayley maps for abelian groups

Journal of Combinatorial Theory Series B
Vertex transitive embeddings of complete graphs

Journal of Combinatorial Theory Series B
Regular t-balanced Cayley maps on semi-dihedral groups

Journal of Combinatorial Theory Series B
Hamiltonian cycles in cubic Cayley graphs: the {2,4k,3} case

Journal of Algebraic Combinatorics: An International Journal
On dihedrants admitting arc-regular group actions

Journal of Algebraic Combinatorics: An International Journal
Regular Cayley maps of skew-type 3 for abelian groups

European Journal of Combinatorics
Representativity of Cayley maps

European Journal of Combinatorics

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Abstract

We present a theory of Cayley maps, i.e., embeddings of Cayley graphs into oriented surfaces having the same cyclic rotation of generators around each vertex. These maps have often been used to encode symmetric embeddings of graphs. We also present an algebraic theory of Cayley maps and we apply the theory to determine exactly which regular or edge-transitive tilings of the sphere or plane are Cayley maps or Cayley graphs. Our main goal, however, is to provide the general theory so as to make it easier for others to study Cayley maps.