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May 2018 The Smallest Self-dual Embeddable Graphs in a Pseudosurface
Ethan Rarity, Steven Schluchter, J. Z. Schroeder
Missouri J. Math. Sci. 30(1): 85-92 (May 2018). DOI: 10.35834/mjms/1534384958

Abstract

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.

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Ethan Rarity. Steven Schluchter. J. Z. Schroeder. "The Smallest Self-dual Embeddable Graphs in a Pseudosurface." Missouri J. Math. Sci. 30 (1) 85 - 92, May 2018. https://doi.org/10.35834/mjms/1534384958

Information

Published: May 2018
First available in Project Euclid: 16 August 2018

zbMATH: 06949053
MathSciNet: MR3844394
Digital Object Identifier: 10.35834/mjms/1534384958

Subjects:
Primary: 05C10

Rights: Copyright © 2018 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.30 • No. 1 • May 2018
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