On families of 2-nearly Platonic graphs

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

doi:10.5614/ejgta.2022.10.2.23

On families of 2-nearly Platonic graphs

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

Mathematics & Statistics

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

Abstract

A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d₁, d₂, both different from d. Such a graph is called balanced if d₁ = d₂. We show that all connected 2-nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.

Original language	English (US)
Pages (from-to)	659-684
Number of pages	26
Journal	Electronic Journal of Graph Theory and Applications
Volume	10
Issue number	2
DOIs	https://doi.org/10.5614/ejgta.2022.10.2.23
State	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022, Electronic Journal of Graph Theory and Applications. All Rights Reserved.

Keywords

Planar graphs
Platonic graphs
Regular graphs

Publisher link

10.5614/ejgta.2022.10.2.23

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abstract = "A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d1, d2, both different from d. Such a graph is called balanced if d1 = d2. We show that all connected 2-nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.",

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AU - Froncek, Dalibor

AU - Khorsandi, Mahdi Reza

AU - Musawi, Seyed Reza

AU - Qiu, Jiangyi

PY - 2022

Y1 - 2022

N2 - A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d1, d2, both different from d. Such a graph is called balanced if d1 = d2. We show that all connected 2-nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.

AB - A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d1, d2, both different from d. Such a graph is called balanced if d1 = d2. We show that all connected 2-nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.

KW - Planar graphs

KW - Platonic graphs

KW - Regular graphs

UR - https://www.scopus.com/pages/publications/85141799284

UR - https://www.scopus.com/pages/publications/85141799284#tab=citedBy

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EP - 684

JO - Electronic Journal of Graph Theory and Applications

JF - Electronic Journal of Graph Theory and Applications

IS - 2

ER -

On families of 2-nearly Platonic graphs

Abstract

Bibliographical note

Keywords

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