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Title: | Bounds on the domination number in oriented graphs |
Authors: | Mostafa, Blidia Lyes, Ould-Rabah |
Keywords: | locating-domination critical graph |
Issue Date: | 7-Nov-2016 |
Series/Report no.: | 2015; |
Abstract: | Abstract A dominating set of an oriented graph D is a set S of vertices of D such that every vertex not in S is a successor of some vertex of S. The minimum cardinality of a dominating set of D; denoted (D), is the domination number of D. An irredundant set of an oriented graph D is a set S of vertices of D such that every vertex of S has a private successor, that is, for all x 2 S; jO[x] O[S x]j 1. The irredundance number of an oriented graph, denoted ir(D), is the least number of vertices in a maximal irredundant set. We denote by (D) and s(D); the number of edges in a maximum matching and support vertices of the underlyng graph of an oriented graph D; respectively. In this paper, we show that for every oriented graph D, s(D) ir(D) (D) 6 n(D) 1 (D). We also give characterizations of oriented trees satisfying (T) = n(T) (T) and oriented graphs satisfying (D) = s(D) and s(D) = n(D) (D); respectively. |
URI: | http://dspace.univ-ouargla.dz/jspui/handle/123456789/12041 |
Appears in Collections: | 1. Faculté des mathématiques et des sciences de la matière |
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File | Description | Size | Format | |
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Bounds on the domination number in oriented.pdf | 203,81 kB | Adobe PDF | View/Open |
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