The non-orientable genus of some metacyclic groups


We 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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Work supported in part by the Research Council of Slovenia, Yugoslavia and NSF Contract DMS-8717441.

Supported by NSF Contract DMS-8601760.

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Pisanski, T., Tucker, T.W. & Witte, D. The non-orientable genus of some metacyclic groups. Combinatorica 12, 77–87 (1992).

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AMS subject classification (1991)

  • 05 C 10
  • 05 C 25
  • 20 F 32