# The non-orientable genus of some metacyclic groups

@article{Pisanski1992TheNG, title={The non-orientable genus of some metacyclic groups}, author={Toma{\vz} Pisanski and Thomas W. Tucker and Dave Witte Morris}, journal={Combinatorica}, year={1992}, volume={12}, pages={77-87} }

AbstractWe describe non-orientable, octagonal embeddings for certain 4-valent, bipartite Cayley graphs of finite metacyclic groups, and give a class of examples for which this embedding realizes the non-orientable genus of the group. This yields a construction of Cayley graphs for which
$$2\gamma - \tilde \gamma $$
is arbitrarily large, where γ and
$$\tilde \gamma $$
are the orientable genus and the non-orientable genus of the Cayley graph.

## One Citation

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