Generating all 3-connected 4-regular planar graphs from the octahedron graph

Haitze J. Broersma; A.J.W. Duijvestijn; A.J.W. Duijvestijn; F. Gobel

doi:10.1002/jgt.3190170508

Generating all 3-connected 4-regular planar graphs from the octahedron graph

Haitze J. Broersma
, A.J.W. Duijvestijn
, A.J.W. Duijvestijn
, F. Gobel

Discrete Mathematics and Mathematical Programming

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

26 Citations (Scopus)

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Abstract

We prove that all 3-connected 4-regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all connected 4-regular planar graphs from the Octahedron Graph.

Original language	English
Pages (from-to)	613-620
Number of pages	8
Journal	Journal of graph theory
Volume	17
Issue number	5
DOIs	https://doi.org/10.1002/jgt.3190170508
Publication status	Published - 1993

Keywords

IR-70999
METIS-140354

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10.1002/jgt.3190170508

Broersma93generating

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title = "Generating all 3-connected 4-regular planar graphs from the octahedron graph",

abstract = "We prove that all 3-connected 4-regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all connected 4-regular planar graphs from the Octahedron Graph.",

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author = "Broersma, \{Haitze J.\} and A.J.W. Duijvestijn and A.J.W. Duijvestijn and F. Gobel",

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AU - Broersma, Haitze J.

AU - Duijvestijn, A.J.W.

AU - Gobel, F.

PY - 1993

Y1 - 1993

N2 - We prove that all 3-connected 4-regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all connected 4-regular planar graphs from the Octahedron Graph.

AB - We prove that all 3-connected 4-regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all connected 4-regular planar graphs from the Octahedron Graph.

KW - IR-70999

KW - METIS-140354

U2 - 10.1002/jgt.3190170508

DO - 10.1002/jgt.3190170508

M3 - Article

SN - 0364-9024

VL - 17

SP - 613

EP - 620

JO - Journal of graph theory

JF - Journal of graph theory

IS - 5

ER -

Generating all 3-connected 4-regular planar graphs from the octahedron graph

Abstract

Keywords

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