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arXiv · 1407.7263

Locating-dominating sets and identifying codes in graphs of girth at least 5

Camino Balbuena·Florent Foucaud·Adriana Hansberg
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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 meet these bounds.

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Camino Balbuena, Florent Foucaud, Adriana Hansberg. 2015-11-24. Locating-dominating sets and identifying codes in graphs of girth at least 5. https://arxiv.org/abs/1407.7263

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