# 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}
}
• Published 1 March 1992
• Mathematics
• Combinatorica
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.
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