Dominating sequences in grid-like and toroidal graphs

Boštjan Brešar, Csilla Bujtás, Tanja Gologranc, Sandi Klavžar, Gašper Košmrlj, Balázs Patkós, Z. Tuza, M. Vizer

Research output: Contribution to journalArticle

3 Citations (Scopus)


A longest sequence S of distinct vertices of a graph G such that each vertex of S dominates some vertex that is not dominated by its preceding vertices, is called a Grundy dominating sequence; the length of S is the Grundy domination number of G. In this paper we study the Grundy domination number in the four standard graph products: the Cartesian, the lexicographic, the direct, and the strong product. For each of the products we present a lower bound for the Grundy domination number which turns out to be exact for the lexicographic product and is conjectured to be exact for the strong product. In most of the cases exact Grundy domination numbers are determined for products of paths and/or cycles.

Original languageEnglish
Article number#P4.34
JournalElectronic Journal of Combinatorics
Issue number4
Publication statusPublished - Dec 9 2016



  • Edge clique cover
  • Graph product
  • Grundy domination
  • Isoperimetric inequality

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this

Brešar, B., Bujtás, C., Gologranc, T., Klavžar, S., Košmrlj, G., Patkós, B., Tuza, Z., & Vizer, M. (2016). Dominating sequences in grid-like and toroidal graphs. Electronic Journal of Combinatorics, 23(4), [#P4.34].