Construction of planar triangulations with minimum degree 5

G. Brinkmann; Brendan D. McKay

doi:10.1016/j.disc.2005.06.019

Construction of planar triangulations with minimum degree 5

G. Brinkmann^*, Brendan D. McKay

^*Corresponding author for this work

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

37 Citations (Scopus)

Abstract

In this article, we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3-connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5.

Original language	English
Pages (from-to)	147-163
Number of pages	17
Journal	Discrete Mathematics
Volume	301
Issue number	2-3
DOIs	https://doi.org/10.1016/j.disc.2005.06.019
Publication status	Published - 6 Oct 2005

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title = "Construction of planar triangulations with minimum degree 5",

abstract = "In this article, we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3-connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5.",

keywords = "Cubic graph, Fullerene, Generation, Planar triangulation",

author = "G. Brinkmann and McKay, {Brendan D.}",

year = "2005",

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language = "English",

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AU - Brinkmann, G.

AU - McKay, Brendan D.

PY - 2005/10/6

Y1 - 2005/10/6

N2 - In this article, we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3-connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5.

AB - In this article, we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3-connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5.

KW - Cubic graph

KW - Fullerene

KW - Generation

KW - Planar triangulation

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DO - 10.1016/j.disc.2005.06.019

M3 - Article

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SP - 147

EP - 163

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2-3

ER -

Construction of planar triangulations with minimum degree 5

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