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On (r,≤2)-Locating-Dominating Codes in the Infinite King Grid

Mikko Pelto, On (r,≤2)-Locating-Dominating Codes in the Infinite King Grid. Advances in Mathematics of Communications 6(1), 27 – 38, 2012.

Abstract:

Assume that G=(V,E) is an undirected graph with vertex set V and edge set E. The ball B_r(v) denotes the vertices within graphical distance r from v. Let I_r(F)=⋃_{v∈F}(B_r(v)∩C) be a set of codewords in the neighbourhoods of vertices v∈F. A subset C⊆V is called 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. A subset C⊆V is an (r,≤l)-locating-dominating code of type B if the sets I_r(F) are distinct for all subsets F⊆V∖C with at most l vertices. We study (r,≤l)-locating-dominating codes in the infinite king grid when r≥1 and l=2. 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,(x1,y1)≠(x2,y2)}.

BibTeX entry:

@ARTICLE{jPelto_Mikko12a,
  title = {On (r,≤2)-Locating-Dominating Codes in the Infinite King Grid},
  author = {Pelto, Mikko},
  journal = {Advances in Mathematics of Communications},
  volume = {6},
  number = {1},
  pages = {27 – 38},
  year = {2012},
  keywords = {Locating-dominating code, king grid, graph, density},
}

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

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