A note on nearly Platonic graphs with connectivity one

Dalibor Froncek (Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, Minnesota 55812, U.S.A.)
Mahdi Reza Khorsandi (Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 36199-95161, Shahrood, Iran)
Seyed Reza Musawi (Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 36199-95161, Shahrood, Iran)
Jiangyi Qiu (Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, U.S.A)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications

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.