Geodesic
Locating-dominating sets and identifying codes in graphs of girth at least 5
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locating-dominating set or identifying code for graphs of girth at least 5 and of given minimum degree. We use the technique of vertex-disjoint paths to provide upper bounds on the minimum size of such sets, and construct graphs who come close to meeting these bounds.
DOI : 10.37236/4562
Classification : 05C69, 05C35, 05C07
Mots-clés : identifying codes, locating-dominating sets, dominating sets, path covers, girth, minimum degree 
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     author = {Camino Balbuena and Florent Foucaud and Adriana Hansberg},
     title = {Locating-dominating sets and identifying codes in graphs of girth at least 5},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {2},
     doi = {10.37236/4562},
     zbl = {1311.05144},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4562/}
}
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Camino Balbuena; Florent Foucaud; Adriana Hansberg. Locating-dominating sets and identifying codes in graphs of girth at least 5. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4562

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