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Stack Domination Density

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Abstract

There are infinite sequences of graphs {G n } where |G n | = n such that the minimal dominating sets for G i × H fall into predictable patterns, in light of which γ (G n × 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 {G n } consists of cycles or path is explored in detail, and the domination density of the Grötzsch graph is calculated. For several other sequences {G n }, 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.

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Authors and Affiliations

  1. Department of Mathematics, Manchester University, North Manchester, IN, 46962, USA

    Timothy Brauch

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Paul Horn

  3. Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA

    Adam Jobson & D. Jacob Wildstrom

Authors
  1. Timothy Brauch
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  2. Paul Horn
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  3. Adam Jobson
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  4. D. Jacob Wildstrom
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Correspondence to D. Jacob Wildstrom.

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Brauch, T., Horn, P., Jobson, A. et al. Stack Domination Density. Graphs and Combinatorics 29, 1689–1711 (2013). https://doi.org/10.1007/s00373-012-1219-2

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  • DOI: https://doi.org/10.1007/s00373-012-1219-2

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