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