Name
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^L^D(P\"n), satisfies M\"r^L^D(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^L^D(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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.disc.2011.05.004 | Discrete Mathematics |
Keywords | DocType | Volume |
path,optimal code,locating–dominating code,domination,graph,locating-dominating code,code optimization,satisfiability | Journal | 311 |
Issue | ISSN | Citations |
17 | Discrete Mathematics | 2 |
PageRank | References | Authors |
0.40 | 11 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Geoffrey Exoo | 1 | 187 | 39.86 |
| Ville Junnila | 2 | 43 | 10.51 |
| Tero Laihonen | 3 | 363 | 39.39 |