Balanced 3-nearly Platonic graphs

Dalibor Froncek; Jiangyi Qiu

Balanced 3-nearly Platonic graphs

Dalibor Froncek
, Jiangyi Qiu

Mathematics & Statistics

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

3 Scopus citations

Abstract

A balanced 3-nearly Platonic graph of type (k, d) is a kregular planar graph with three faces of the same degree m, and all f − 3 remaining faces of degree d 6= m. We present constructions of infinite families of balanced 3-nearly Platonic graph of type (k, d) for all admissible pairs (k, d), whose existence was claimed by Deza, Dutour Sikirič, and Shtogrin in 2013.

Original language	English (US)
Pages (from-to)	34-63
Number of pages	30
Journal	Bulletin of the Institute of Combinatorics and its Applications
Volume	86
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019,Bulletin of the Institute of Combinatorics and its Applications.All Rights Reserved.

Keywords

Planar graphs
Platonic graphs
regular graphs

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title = "Balanced 3-nearly Platonic graphs",

abstract = "A balanced 3-nearly Platonic graph of type (k, d) is a kregular planar graph with three faces of the same degree m, and all f − 3 remaining faces of degree d 6= m. We present constructions of infinite families of balanced 3-nearly Platonic graph of type (k, d) for all admissible pairs (k, d), whose existence was claimed by Deza, Dutour Sikiri{\v c}, and Shtogrin in 2013.",

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author = "Dalibor Froncek and Jiangyi Qiu",

year = "2019",

language = "English (US)",

volume = "86",

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journal = "Bulletin of the Institute of Combinatorics and its Applications",

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TY - JOUR

T1 - Balanced 3-nearly Platonic graphs

AU - Froncek, Dalibor

AU - Qiu, Jiangyi

PY - 2019

Y1 - 2019

N2 - A balanced 3-nearly Platonic graph of type (k, d) is a kregular planar graph with three faces of the same degree m, and all f − 3 remaining faces of degree d 6= m. We present constructions of infinite families of balanced 3-nearly Platonic graph of type (k, d) for all admissible pairs (k, d), whose existence was claimed by Deza, Dutour Sikirič, and Shtogrin in 2013.

AB - A balanced 3-nearly Platonic graph of type (k, d) is a kregular planar graph with three faces of the same degree m, and all f − 3 remaining faces of degree d 6= m. We present constructions of infinite families of balanced 3-nearly Platonic graph of type (k, d) for all admissible pairs (k, d), whose existence was claimed by Deza, Dutour Sikirič, and Shtogrin in 2013.

KW - Planar graphs

KW - Platonic graphs

KW - regular graphs

UR - https://www.scopus.com/pages/publications/85094055998

UR - https://www.scopus.com/pages/publications/85094055998#tab=citedBy

M3 - Article

AN - SCOPUS:85094055998

SN - 1183-1278

VL - 86

SP - 34

EP - 63

JO - Bulletin of the Institute of Combinatorics and its Applications

JF - Bulletin of the Institute of Combinatorics and its Applications

ER -

Balanced 3-nearly Platonic graphs

Abstract

Bibliographical note

Keywords

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