A note on nearly Platonic graphs with connectivity one

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

doi:10.5614/ejgta.2021.9.1.17

Electronic Journal of Graph Theory and Applications (Apr 2021)

A note on nearly Platonic graphs with connectivity one

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

Affiliations

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

DOI: https://doi.org/10.5614/ejgta.2021.9.1.17
Journal volume & issue: Vol. 9, no. 1
pp. 195 – 205

Abstract

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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.

planar graph, regular graph, platonic graph

Published in Electronic Journal of Graph Theory and Applications

ISSN: 2338-2287 (Print)
Publisher: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
Country of publisher: Indonesia
LCC subjects: Science: Mathematics
Website: http://www.ejgta.org/

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