## Abstract We prove that all 3βconnected 4βregular 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 con
Generating 5-regular planar graphs
β Scribed by Guoli Ding; Jinko Kanno; Jianning Su
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 210 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
For k=0, 1, 2, 3, 4, 5, let ${\cal{P}}_{k}$ be the class of k βedgeβconnected 5βregular planar graphs. In this paper, graph operations are introduced that generate all graphs in each ${\cal{P}}_{k}$. Β© 2009 Wiley Periodicals, Inc. J Graph Theory 61: 219β240, 2009
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## Abstract It has been communicated by P. Manca in this journal that all 4βregular 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.
## Abstract All planar connected graphs regular of degree four can be generated from the graph of the octahedron, using four operations.
Let G be chosen uniformly at random from the set G G r, n of r-regular graphs w x Ε½ . with vertex set n . We describe polynomial time algorithms that whp i find a Ε½ . Hamilton cycle in G, and ii approximately count the number of Hamilton cycles in G.