On Genus of Circulant Graphs

Properties of circulant graphs have being studied by many authors, but just a few results concerning their genus characterization were presented up to now. We can quote the classification of all circulant planar graphs given by C. Heuberger in 2003, some previous results by the authors showing that any circulant graph of order four must be either genus one or zero and the existence of order 6 circulant graphs of arbitrarily high genus. We present here a complete classification of circulant graphs of genus one, derive a general lower bound for the genus of a circulant graph and construct a family of circulant graphs which reach this bound.