A note on nearly platonic graphs

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

A note on nearly platonic graphs

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

Mathematics & Statistics

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

4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	86-103
Number of pages	18
Journal	Australasian Journal of Combinatorics
Volume	70
Issue number	1
State	Published - Feb 2018

Bibliographical note

Publisher Copyright:
© 2018, University of Queensland. All rights reserved.

OpenUrl availability

Full text

Cite this

@article{078da4bc814041f6b6943e279d19e28e,

title = "A note on nearly platonic graphs",

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.",

author = "Keith, {William J.} and Dalibor Froncek and Kreher, {Donald L.}",

year = "2018",

month = feb,

language = "English (US)",

volume = "70",

pages = "86--103",

journal = "Australasian Journal of Combinatorics",

issn = "1034-4942",

publisher = "University of Queensland Press",

number = "1",

}

TY - JOUR

T1 - A note on nearly platonic graphs

AU - Keith, William J.

AU - Froncek, Dalibor

AU - Kreher, Donald L.

PY - 2018/2

Y1 - 2018/2

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.

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

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

M3 - Article

AN - SCOPUS:85034421427

SN - 1034-4942

VL - 70

SP - 86

EP - 103

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

IS - 1

ER -

A note on nearly platonic graphs

Abstract

Bibliographical note

OpenUrl availability

Other files and links

Fingerprint

Cite this