A note on nearly Platonic graphs with connectivity one

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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)195-205
Number of pages11
JournalElectronic Journal of Graph Theory and Applications
Volume9
Issue number1
DOIs
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021

Keywords

  • planar graph
  • Platonic graph
  • regular graph

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