Locating-dominating sets and identifying codes in graphs of girth at least 5
Combinatorics
2015-11-25 v2 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1407.7263,
title = {Locating-dominating sets and identifying codes in graphs of girth at least 5},
author = {Camino Balbuena and Florent Foucaud and Adriana Hansberg},
journal= {arXiv preprint arXiv:1407.7263},
year = {2015}
}
Comments
20 pages, 9 figures