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Domination in Graphs of Minimum Degree at least Two and Large Girth

✍ Scribed by Christian Löwenstein; Dieter Rautenbach

Publisher
Springer Japan
Year
2008
Tongue
English
Weight
116 KB
Volume
24
Category
Article
ISSN
0911-0119

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✍ William McCuaig; Bruce Shepherd 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 545 KB

The domination number y ( G ) of a graph G = (V E ) is the minimum cardinality of a subset of Vsuch that every vertex is either in the set or is adjacent to some vertex in the set. We show that if a connected graph G has minimum2degree two and is not one of seven exceptional graphs, then y ( g ) I ~

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A dominating set for a graph G = (V, E) is a subset of vertices V ⊆ V such that for all v ∈ V -V there exists some u ∈ V for which {v, u} ∈ E. The domination number of G is the size of its smallest dominating set(s). We show that for almost all connected graphs with minimum degree at least 2 and q e