Graphs and Combinatorics

, Volume 29, Issue 6, pp 1689–1711

Stack Domination Density


  • Timothy Brauch
    • Department of MathematicsManchester University
  • Paul Horn
    • Department of MathematicsHarvard University
  • Adam Jobson
    • Department of MathematicsUniversity of Louisville
    • Department of MathematicsUniversity of Louisville
Original Paper

DOI: 10.1007/s00373-012-1219-2

Cite this article as:
Brauch, T., Horn, P., Jobson, A. et al. Graphs and Combinatorics (2013) 29: 1689. doi:10.1007/s00373-012-1219-2


There are infinite sequences of graphs {Gn} where |Gn| = n such that the minimal dominating sets for Gi × H fall into predictable patterns, in light of which γ (Gn × H) may be nearly linear in n; the coefficient of linearity may be regarded as the average density of the dominating set in the H-fibers of the product. The specific cases where the sequence {Gn} consists of cycles or path is explored in detail, and the domination density of the Grötzsch graph is calculated. For several other sequences {Gn}, the limit of this density can be seen to exist; in other cases the ratio \({\frac{\gamma (G_n \times H)}{\gamma (G_n)}}\) proves to be of greater interest, and also exists for several families of graphs.


Domination numberCartesian productGrötzsch graphAsymptotic densityAdditive graphsRandom graphs

Mathematics Subject Classification (2000)


Copyright information

© Springer 2012