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

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. [Copyright &y& Elsevier]