A circulant of order $n$ is a Cayley graph for the cyclic group $\mathbb{Z}_n$, and as such, admits a transitive action of $\mathbb{Z}_n$ on its vertices. This paper concerns 2-cell embeddings of connected circulants on closed orientable surfaces. Embeddings on the sphere (the planar case) were classified by Heuberger (2003), and by a theorem of Thomassen (1991), there are only finitely many vertex-transitive graphs with minimum genus $g$, for any given integer $g \ge 3$. Here we completely determine all connected circulants with minimum genus 1 or 2; this corrects and extends an attempted classification of all toroidal circulants by Costa, Strapasson, Alves and Carlos (2010).
@article{10_37236_4013,
author = {Marston Conder and Ricardo Grande},
title = {On embeddings of circulant graphs},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/4013},
zbl = {1325.05059},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4013/}
}
TY - JOUR
AU - Marston Conder
AU - Ricardo Grande
TI - On embeddings of circulant graphs
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4013/
DO - 10.37236/4013
ID - 10_37236_4013
ER -
%0 Journal Article
%A Marston Conder
%A Ricardo Grande
%T On embeddings of circulant graphs
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4013/
%R 10.37236/4013
%F 10_37236_4013
Marston Conder; Ricardo Grande. On embeddings of circulant graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4013
