The problem of determining the domination number of a graph is a well known NPhard problem, even when restricted to planar graphs. By adding a further restriction on the diameter of the graph, we prove that planar graphs with diameter two and three have bounded domination numbers. This implies that
โฆ LIBER โฆ
Planar domination graphs
โ Scribed by Elaine M. Eschen; William F. Klostermeyer; R. Sritharan
- Book ID
- 108315837
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 126 KB
- Volume
- 268
- Category
- Article
- ISSN
- 0012-365X
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## Abstract MacGillivray and Seyffarth (J Graph Theory 22 (1996), 213โ229) 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
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