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**The smallest self-dual embeddable graphs in a pseudosurface.**
*(English)*
Zbl 1396.05083

Summary: A proper embedding of a graph \(G\) in a pseudosurface \(P\) is an embedding in which the regions of the complement of \(G\) in \(P\) are homeomorphic to discs and a vertex of \(G\) appears at each pinchpoint of \(P\); we say that a proper embedding of \(G\) in \(P\) is self dual if there exists an isomorphism from \(G\) to its topological dual. We determine five possible graphs with 7 vertices and 13 edges that could be self-dual embeddable in the pinched sphere, and we establish, by way of computer-powered methods, that such a self-embedding exists for exactly two of these five graphs.

### MSC:

05C60 | Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) |

05C10 | Planar graphs; geometric and topological aspects of graph theory |

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\textit{E. Rarity} et al., Missouri J. Math. Sci. 30, No. 1, 85--92 (2018; Zbl 1396.05083)

Full Text:
Euclid

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