𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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

✍ Scribed by H. J. Broersma; A. J. W. Duijvestijn; F. Göbel

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
384 KB
Volume
17
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

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. © 1993 John Wiley & Sons, Inc.

📜 SIMILAR VOLUMES

Generating all 4-regular planar graphs f
Generating all 4-regular planar graphs from the graph of the octahedron
✍ Jenö Lehel 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB 👁 1 views

## Abstract It has been communicated by P. Manca in this journal that all 4‐regular connected planar graphs can be generated from the graph of the octahedron using simple planar graph operations. We point out an error in the generating procedure and correct it by including an additional operation.

Regular graphs constructed from the clas
Regular graphs constructed from the classical generalized quadrangle Q(4, q)
✍ L. Beukemann; K. Metsch 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB 👁 1 views

Let c k be the smallest number of vertices in a regular graph with valency k and girth 8. It is known that c k+1 ≥ 2(1+k+k 2 +k 3 ) with equality if and only if there exists a finite generalized quadrangle of order k. No such quadrangle is known when k is not a prime power. In this case, small regul