Locating–dominating codes in paths |
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| Authors: | Geoffrey Exoo Ville Junnila Tero Laihonen |
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| Institution: | aDepartment of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA;bTurku Centre for Computer Science TUCS, Finland;cDepartment of Mathematics, University of Turku, FI-20014 Turku, Finland |
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| Abstract: | Bertrand, Charon, Hudry and Lobstein studied, in their paper in 2004 1], r-locating–dominating codes in paths Pn. They conjectured that if r≥2 is a fixed integer, then the smallest cardinality of an r-locating–dominating code in Pn, denoted by  , satisfies  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  for all n≥nr when nr is large enough. In addition, we solve a conjecture on location–domination with segments of even length in the infinite path. |
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| Keywords: | Locating&ndash dominating code Optimal code Domination Graph Path |
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