## 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

### Keywords:

hypermap; hyperface; reflexive hypermaps
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### References:

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