Abstract
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.
Original language | English (US) |
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Pages (from-to) | 195-205 |
Number of pages | 11 |
Journal | Electronic Journal of Graph Theory and Applications |
Volume | 9 |
Issue number | 1 |
DOIs | |
State | Published - Apr 15 2021 |
Bibliographical note
Publisher Copyright:© 2021
Keywords
- Platonic graph
- planar graph
- regular graph