Counting unlabelled toroidal graphs with no K33-subdivisions
<|reference_start|>Counting unlabelled toroidal graphs with no K33-subdivisions: We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of core graphs. Using structure theorems for toroidal and projective-planar graphs containing no K33-subdivisions, we apply these techniques to obtain their unlabelled enumeration.<|reference_end|>
@article{gagarin2005counting,
    title={Counting unlabelled toroidal graphs with no K33-subdivisions},
    author={Andrei Gagarin, Gilbert Labelle, Pierre Leroux (LaCIM, Universite du
  Quebec a Montreal)},
    journal={Adv. in Appl. Math. 39 (2007), no. 1, pp. 51-75},
    year={2005},
    doi={10.1016/j.aam.2006.05.006},
    archivePrefix={arXiv},
    eprint={math/0509004},
    primaryClass={math.CO cs.DM}
}