Grundy domination and zero forcing in Kneser graphs


  • Boštjan Brešar University of Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Slovenia
  • Tim Kos Institute of Mathematics, Physics and Mechanics, Slovenia
  • Pablo Daniel Torres Universidad Nacional de Rosario, Argentina and Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina



Grundy domination number, Grundy total domination number, Kneser graph, zero forcing number, minimum rank


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 γgrt(Kn, r) equals (2r choose 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 choose r) − (2r choose 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.