Artículo
Grundy domination and zero forcing in Kneser graphs
Fecha de publicación:
06/2019
Editorial:
Open Journal Systems
Revista:
Ars Mathematica Contemporanea
ISSN:
1855-3966
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers in the well-known class of Kneser graphs Kn,r. In particular, we establish that the Grundy total domination number γ t gr(Kn,r) equals 2r r for any r ≥ 2 and n ≥ 2r + 1. For the Grundy domination number of Kneser graphs we get γgr(Kn,r) = α(Kn,r) whenever n is sufficiently larger than r. On the other hand, the zero forcing number Z(Kn,r) is proved to be n r − 2r r when n ≥ 3r + 1 and r ≥ 2, while lower and upper bounds are provided for Z(Kn,r) when 2r + 1 ≤ n ≤ 3r. Some lower bounds for different types of minimum ranks of Kneser graphs are also obtained along the way.
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Articulos(CCT - ROSARIO)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - ROSARIO
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - ROSARIO
Citación
Bresar, Bostjan; Kos, Tim; Torres, Pablo Daniel; Grundy domination and zero forcing in Kneser graphs; Open Journal Systems; Ars Mathematica Contemporanea; 17; 2; 6-2019; 419-430
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