A note on nearly Platonic graphs with connectivity one

Dalibor Froncek, Mahdi Reza Khorsandi, Seyed Reza Musawi, Jiangyi Qiu


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.


planar graph, regular graph, Platonic graph

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DOI: http://dx.doi.org/10.5614/ejgta.2021.9.1.17


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