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The reflexible hypermaps of characteristic \(-2\). (English) Zbl 1053.05504

The author classifies the finite reflexible hypermaps with one and two hyperfaces and proves that there is, up to isomorphism, only one non-orientable reflexible hypermap with one hyperface of valency \(n\). This hypermap is projective. The author proves that there are only two non-orientable reflexive hypermaps with two hyperfaces, also both projective. The main result is the classification of reflexible hypermaps of characteristic \(-2\). It is shown that there are \(43\) reflexible hypermaps (ten of them are maps) on orientable surfaces and fifteen hypermaps (twelve maps) on non-orientable surfaces, respectively.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
57M15 Relations of low-dimensional topology with graph theory
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References:

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