A note on nearly platonic graphs

William J. Keith, Dalibor Froncek, Donald L. Kreher

Research output: Research - peer-reviewArticle

Abstract

We define a nearly platonic graph to be a finite k-regular simple planar graph in which all but a small number of the faces have the same degree. we show that it is impossible for such a graph to have exactly one disparate face, and offer some conjectures, including the conjecture that nearly platonic graphs with two disparate faces come in a small set of families.

LanguageEnglish (US)
Pages86-103
Number of pages18
JournalAustralasian Journal of Combinatorics
Volume70
Issue number1
StatePublished - Feb 1 2018

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Face
Graph in graph theory
Simple Graph
Planar graph
Family

Cite this

Keith, W. J., Froncek, D., & Kreher, D. L. (2018). A note on nearly platonic graphs. Australasian Journal of Combinatorics, 70(1), 86-103.

A note on nearly platonic graphs. / Keith, William J.; Froncek, Dalibor; Kreher, Donald L.

In: Australasian Journal of Combinatorics, Vol. 70, No. 1, 01.02.2018, p. 86-103.

Research output: Research - peer-reviewArticle

Keith, WJ, Froncek, D & Kreher, DL 2018, 'A note on nearly platonic graphs' Australasian Journal of Combinatorics, vol 70, no. 1, pp. 86-103.
Keith, William J. ; Froncek, Dalibor ; Kreher, Donald L./ A note on nearly platonic graphs. In: Australasian Journal of Combinatorics. 2018 ; Vol. 70, No. 1. pp. 86-103
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