Locating-dominating codes in cycles.
Geoffrey Exoo, Ville Junnila, Tero K Laihonen · 2011
The smallest cardinality of an r-locating-dominating code in a cycle Cn of length n is denoted by M LD r (Cn). In this paper, we prove that for any r ≥ 5andn ≥ nr when nr is large enough (nr = O(r3)) we have n/3 ≤ M LD r (Cn) ≤ n/3 +1 ifn ≡ 3(mod6)andMLD r (Cn) =⌈n/3⌉ otherwise. Moreover, we determine the exact values of M LD 3 (Cn) and M LD 4 (Cn) for all n.