A1 Refereed original research article in a scientific journal
Locating-dominating codes in paths
Authors: Exoo G, Junnila V, Laihonen T
Publisher: ELSEVIER SCIENCE BV
Publication year: 2011
Journal: Discrete Mathematics
Journal name in source: DISCRETE MATHEMATICS
Journal acronym: DISCRETE MATH
Number in series: 17
Volume: 311
Issue: 17
First page : 1863
Last page: 1873
Number of pages: 11
ISSN: 0012-365X
DOI: https://doi.org/10.1016/j.disc.2011.05.004
Self-archived copy’s web address: https://research.utu.fi/converis/portal/Publication/1348692
Abstract
Bertrand, Charon, Hudry and Lobstein studied, in their paper in 2004 [1] r-locating-dominating codes in paths P(n). They conjectured that if r >= 2 is a fixed integer, then the smallest cardinality of an r-locating-dominating code in P(n), denoted by M(r)(LD) (P(n)), satisfies M(r)(LD)(P(n)) = [(n + 1)/3] for infinitely many values of n. We prove that this conjecture holds. In fact, we show a stronger result saying that for any r >= 3 we have M(r)(LD) (P(n)) = [(n + 1)/3] for all n >= n(r), when n(r) is large enough. In addition, we solve a conjecture on location-domination with segments of even length in the infinite path. (C) 2011 Elsevier B.V. All rights reserved.
Bertrand, Charon, Hudry and Lobstein studied, in their paper in 2004 [1] r-locating-dominating codes in paths P(n). They conjectured that if r >= 2 is a fixed integer, then the smallest cardinality of an r-locating-dominating code in P(n), denoted by M(r)(LD) (P(n)), satisfies M(r)(LD)(P(n)) = [(n + 1)/3] for infinitely many values of n. We prove that this conjecture holds. In fact, we show a stronger result saying that for any r >= 3 we have M(r)(LD) (P(n)) = [(n + 1)/3] for all n >= n(r), when n(r) is large enough. In addition, we solve a conjecture on location-domination with segments of even length in the infinite path. (C) 2011 Elsevier B.V. All rights reserved.
Downloadable publication This is an electronic reprint of the original article. |  |
UTU Research Portal