### 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.

Language | English (US) |
---|---|

Pages | 86-103 |

Number of pages | 18 |

Journal | Australasian Journal of Combinatorics |

Volume | 70 |

Issue number | 1 |

State | Published - Feb 1 2018 |

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### Cite this

*Australasian Journal of Combinatorics*,

*70*(1), 86-103.

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

Research output: Research - peer-review › Article

*Australasian Journal of Combinatorics*, vol 70, no. 1, pp. 86-103.

}

TY - JOUR

T1 - A note on nearly platonic graphs

AU - Keith,William J.

AU - Froncek,Dalibor

AU - Kreher,Donald L.

PY - 2018/2/1

Y1 - 2018/2/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=85034421427&partnerID=8YFLogxK

M3 - Article

VL - 70

SP - 86

EP - 103

JO - Australasian Journal of Combinatorics

T2 - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

IS - 1

ER -