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

A note on nearly Platonic graphs with connectivity one

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

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	195-205
Number of pages	11
Journal	Electronic Journal of Graph Theory and Applications
Volume	9
Issue number	1
DOIs	https://doi.org/10.5614/ejgta.2021.9.1.17
State	Published - Apr 15 2021

Bibliographical note

Publisher Copyright:
© 2021

Keywords

Platonic graph
planar graph
regular graph

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10.5614/ejgta.2021.9.1.17

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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.",

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AU - Khorsandi, Mahdi Reza

AU - Musawi, Seyed Reza

AU - Qiu, Jiangyi

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Y1 - 2021/4/15

N2 - 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.

AB - 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.

KW - Platonic graph

KW - planar graph

KW - regular graph

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A note on nearly Platonic graphs with connectivity one

Abstract

Bibliographical note

Keywords

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