Locating-Dominating Sets and Identifying Codes in Graphs of Girth at least 5

Camino Balbuena, Florent Foucaud, Adriana Hansberg

Abstract


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.


Keywords


Identifying codes; Locating-dominating sets; Dominating sets; Path covers; Girth; Minimum degree

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