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A note on domination parameters of the conjunction of two special graphs

100%
Zwierzchowski M.
Discussiones Mathematicae Graph Theory
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2001
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tom 21
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nr 2
303-310
EN
A dominating set D of G is called a split dominating set of G if the subgraph induced by the subset V(G)-D is disconnected. The cardinality of a minimum split dominating set is called the minimum split domination number of G. Such subset and such number was introduced in [4]. In [2], [3] the authors estimated the domination number of products of graphs. More precisely, they were study products of paths. Inspired by those results we give another estimation of the domination number of the conjunction (the cross product) Pₙ ∧ G. The split domination number of Pₙ ∧ G also is determined. To estimate this number we use the minimum connected domination number $γ_c(G)$.
2
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Note on the split domination number of the Cartesian product of paths

100%
Zwierzchowski M.
Discussiones Mathematicae Graph Theory
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2005
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tom 25
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nr 1-2
79-84
EN
In this note the split domination number of the Cartesian product of two paths is considered. Our results are related to [2] where the domination number of Pₘ ☐ Pₙ was studied. The split domination number of P₂ ☐ Pₙ is calculated, and we give good estimates for the split domination number of Pₘ ☐ Pₙ expressed in terms of its domination number.
3
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Domination parameters of a graph with deleted special subset of edges

63%
Kwaśnik M., Zwierzchowski M.
Discussiones Mathematicae Graph Theory
|
2001
|
tom 21
|
nr 2
229-238
EN
This paper contains a number of estimations of the split domination number and the maximal domination number of a graph with a deleted subset of edges which induces a complete subgraph Kₚ. We discuss noncomplete graphs having or not having hanging vertices. In particular, for p = 2 the edge deleted graphs are considered. The motivation of these problems comes from [2] and [6], where the authors, among other things, gave the lower and upper bounds on irredundance, independence and domination numbers of an edge deleted graph.
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