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| On Trees with Double Domination Number Equal to the 2-Outer-Independent Domination Number Plus One |
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Citation： |
Marcin KRZYWKOWSKI.On Trees with Double Domination Number Equal to the 2-Outer-Independent Domination Number Plus One[J].Chinese Annals of Mathematics B,2012,33(1):113~126 |
| Page view： 2608
Net amount： 2736 |
Authors： |
Marcin KRZYWKOWSKI; |
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| Abstract： |
A vertex of a graph is said to dominate itself and all of its neighbors. A doubledominating set of a graph G is a set D of vertices of G, such that every vertex of G isdominated by at least two vertices of D. The double domination number of a graph Gis the minimum cardinality of a double dominating set of G. For a graph G = (V,E),a subset D ? V (G) is a 2-dominating set if every vertex of V (G) \ D has at least twoneighbors in D, while it is a 2-outer-independent dominating set of G if additionally the setV (G)\D is independent. The 2-outer-independent domination number of G is the minimumcardinality of a 2-outer-independent dominating set of G. This paper characterizes all treeswith the double domination number equal to the 2-outer-independent domination numberplus one. |
Keywords： |
Double domination, 2-Outer-independent domination, 2-Domination, Tree |
Classification： |
05C05,05C69 |
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