A1 Refereed original research article in a scientific journal
Optimal (r, <= 3)-locating-dominating codes in the infinite king grid
Authors: Pelto M
Publisher: ELSEVIER SCIENCE BV
Publication year: 2013
Journal: Discrete Applied Mathematics
Journal name in source: DISCRETE APPLIED MATHEMATICS
Journal acronym: DISCRETE APPL MATH
Number in series: 16-17
Volume: 161
Issue: 16-17
First page : 2597
Last page: 2603
Number of pages: 7
ISSN: 0166-218X
DOI: https://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.
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.
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