A note on nearly Platonic graphs with connectivity one

A note on nearly Platonic graphs with connectivity one

A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek, and Kreher on non-existence of 2-connected n...

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Veröffentlicht in:Electronic journal of graph theory and applications 2021-01, Vol.9 (1), p.195-205
Hauptverfasser: Froncek, Dalibor, Khorsandi, Mahdi Reza, Musawi, Seyed Reza, Qiu, Jiangyi
Format: Artikel
Sprache:eng
Schlagworte:
planar graph, regular graph, platonic graph
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Zusammenfassung:A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek, and Kreher on non-existence of 2-connected nearly Platonic graphs.
ISSN:2338-2287
2338-2287
DOI:10.5614/ejgta.2021.9.1.17