Characterising planar Cayley graphs and Cayley complexes in terms of group presentations

Authors:
Agelos Georgakopoulos
Affiliations:
-
Venue:
European Journal of Combinatorics
Year:
2014

Citing 3
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Abstract

We prove that a Cayley graph can be embedded in the Euclidean plane without accumulation points of vertices if and only if it is the 1-skeleton of a Cayley complex that can be embedded in the plane after removing redundant simplices. We also give a characterisation of these Cayley graphs in term of group presentations, and deduce that they can be effectively enumerated.