English

A note on nearly Platonic graphs with connectivity one

Combinatorics 2020-06-15 v4

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.

Keywords

Cite

@article{arxiv.1911.05135,
  title  = {A note on nearly Platonic graphs with connectivity one},
  author = {D. Froncek and M. R. Khorsandi and S. R. Musawi and J. Qiu},
  journal= {arXiv preprint arXiv:1911.05135},
  year   = {2020}
}

Comments

We made some changes in notation, added figures, and updated some proofs

R2 v1 2026-06-23T12:13:34.733Z