## Abstract MacGillivray and Seyffarth (J Graph Theory 22 (1996), 213β229) proved that planar graphs of diameter two have domination number at most three and planar graphs of diameter three have domination number at most ten. They also give examples of planar graphs of diameter four having arbitrar
β¦ LIBER β¦
Power domination in planar graphs with small diameter
β Scribed by Min Zhao; Li-ying Kang
- Book ID
- 107482481
- Publisher
- Chinese Electronic Periodical Services
- Year
- 2007
- Tongue
- English
- Weight
- 263 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1007-6417
No coin nor oath required. For personal study only.
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We consider the maximum number of vertices in a cubic graph with small diameter. We show that a cubic graph of diameter 4 has at most 40 vertices. (The Moore bound is 46 and graphs with 38 vertices are known.) We also consider bipartite cubic graphs of diameter 5, for which the Moore bound is 62. We