Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647954 | Discrete Mathematics | 2011 | 11 Pages |
Abstract
Bertrand, Charon, Hudry and Lobstein studied, in their paper in 2004 [1], rr-locating–dominating codes in paths PnPn. They conjectured that if r≥2r≥2 is a fixed integer, then the smallest cardinality of an rr-locating–dominating code in PnPn, denoted by MrLD(Pn), satisfies MrLD(Pn)=⌈(n+1)/3⌉ for infinitely many values of nn. We prove that this conjecture holds. In fact, we show a stronger result saying that for any r≥3r≥3 we have MrLD(Pn)=⌈(n+1)/3⌉ for all n≥nrn≥nr when nrnr is large enough. In addition, we solve a conjecture on location–domination with segments of even length in the infinite path.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Geoffrey Exoo, Ville Junnila, Tero Laihonen,