A note on nearly Platonic graphs with connectivity one

A note on nearly Platonic graphs with connectivity one

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 n...

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Main Authors: Froncek, Dalibor; Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, Minnesota 55812, U.S.A (Author), Khorsandi, Mahdi Reza; Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 6199-95161, Shahrood, Iran (Author), Musawi, Seyed Reza; Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 6199-95161, Shahrood, Iran (Author), Qiu, Jiangyi; Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 1003-9305, U.S.A (Author)
Format: EJournal Article
Published: GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2021-04-15.
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info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Peer-reviewed Article
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Summary: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.
Item Description:https://www.ejgta.org/index.php/ejgta/article/view/1115

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