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On Locating-Dominating Codes for Locating Large Numbers of Vertices in the Infinite King Grid

Mikko Pelto, On Locating-Dominating Codes for Locating Large Numbers of Vertices in the Infinite King Grid. The Australasian Journal of Combinatorics 50, 127-139, 2011.

Abstract:

Assume that G = (V,E) is an undirected graph with vertex set V and edge set E. The ball Br(v) denotes the vertices within graphical distance r from v. A subset C ⊆ V is called an (r,≤ l)-locating-dominating code of type B if the sets I_r(F) = ∪_{v∈F} (Br(v) ∩ C) are distinct for all subsets F ⊆ V \C with at most l vertices. A subset C ⊆ V is an (r,≤ l)-locating-dominating code of type A if sets I_r(F1) and I_r(F2) are distinct for all subsets F1, F2 ⊆ V where F1 != F2, F1 ∩ C = F2 ∩ C and |F1|, |F2| ≤ l. We study (r,≤ l)-locating-dominating codes in the infinite king grid when r ≥ 1 and l ≥ 3. The infinite king grid is the graph with vertex set Z^2 and edge set {{(x1, y1), (x2, y2)} | |x1 − x2| ≤ 1, |y1 − y2| ≤ 1}.

BibTeX entry:

@ARTICLE{jPelto_Mikko11a,
  title = {On Locating-Dominating Codes for Locating Large Numbers of Vertices in the Infinite King Grid},
  author = {Pelto, Mikko},
  journal = {The Australasian Journal of Combinatorics},
  volume = {50},
  pages = {127-139},
  year = {2011},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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