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.
CitacióBalbuena, C., Foucaud, F., Hansberg, A. Locating-dominating sets and identifying codes in Graphs of Girth at least 5. "Electronic journal of combinatorics", 29 Abril 2015, vol. 22, núm. 2, p. 1-22.