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Optimal (r, <= 3)-Locating-Dominating Codes in the Infinite King Grid

Mikko Pelto, Optimal (r, <= 3)-Locating-Dominating Codes in the Infinite King Grid. 161, 2597–2603, 2013.

http://dx.doi.org/10.1016/j.dam.2013.04.027

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. A subset C subset of V is called an (r, <= l)-Locating-dominating code of type B if the sets I-r(F) = boolean OR(v is an element of F)(B-r(v) boolean AND C) are distinct for all subsets F subset of V \ C with at most I vertices. We give examples of optimal (r, < 3)-locating-dominating codes of type B in the infinite king grid for all r is an element of N+ and prove optimality. The infinite king grid is the graph with vertex set Z(2) and edge set {{(x(1), y(1)), (x(2), y(2))} vertical bar vertical bar x(1) - x(2)vertical bar <= 1, vertical bar y(1) - y(2)vertical bar <= 1}. (C) 2013 Elsevier B.V. All rights reserved.

BibTeX entry:

@ARTICLE{uconv1469106,
  title = {Optimal (r, <= 3)-Locating-Dominating Codes in the Infinite King Grid},
  author = {Pelto, Mikko},
  volume = {161},
  publisher = {ELSEVIER SCIENCE BV},
  pages = {2597–2603},
  year = {2013},
  keywords = {Locating-dominating code;King grid;Graph;Density},
  ISSN = {0166-218X},
}

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

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