A1 Refereed original research article in a scientific journal
Locating-dominating codes in cycles
Authors: Exoo G, Junnila V, Laihonen T
Publisher: University of Queensland Press
Publication year: 2011
Journal: Australasian Journal of Combinatorics
Volume: 49
First page : 177
Last page: 194
Number of pages: 18
ISSN: 1034-4942
Web address : https://ajc.maths.uq.edu.au/pdf/49/ajc_v49_p177.pdf
Self-archived copy’s web address: https://research.utu.fi/converis/portal/Publication/2586672
Abstract
The smallest cardinality of an r-locating-dominating code in a cycle C_n of length n is denoted by M_r^{LD}(C_n). In this paper, we prove that for any r geq 5 and n geq n_r when n_r is large enough (n_r=mathcal{O}(r^3)) we have n/3 leq M_r^{LD}(C_n) leq n/3+1 if n equiv 3 pmod{6} and M_r^{LD}(C_n) = lceil n/3
ceil otherwise. Moreover, we determine the exact values of M_3^{LD}(C_n) and M_4^{LD}(C_n) for all n.
The smallest cardinality of an r-locating-dominating code in a cycle C_n of length n is denoted by M_r^{LD}(C_n). In this paper, we prove that for any r geq 5 and n geq n_r when n_r is large enough (n_r=mathcal{O}(r^3)) we have n/3 leq M_r^{LD}(C_n) leq n/3+1 if n equiv 3 pmod{6} and M_r^{LD}(C_n) = lceil n/3
ceil otherwise. Moreover, we determine the exact values of M_3^{LD}(C_n) and M_4^{LD}(C_n) for all n.
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