# Minimum-Density Identifying Codes in Square Grids

• Marwane Bouznif
• Frédéric Havet
• Myriam Preissmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9778)

## Abstract

An identifying code in a graph G is a subset of vertices with the property that for each vertex $$v \in V(G)$$, the collection of elements of C at distance at most 1 from v is non-empty and distinct from the collection of any other vertex. We consider the minimum density $$d^*(\mathcal{S}_k)$$ of an identifying code in the square grid $$\mathcal{S}_k$$ of height k (i.e. with vertex set $$\mathbb {Z} \times \{1, \dots , k\}$$). Using the Discharging Method, we prove $$\displaystyle \frac{7}{20} + \frac{1}{20k} \le d^*(\mathcal{S}_k) \le \min \left\{ \frac{2}{5}, \frac{7}{20} + \frac{3}{10k} \right\}$$, and $$\displaystyle d^*(\mathcal{S}_3) =\frac{7}{18}$$.

### Keywords

Identifying code Square grid Discharging method

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© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• Marwane Bouznif
• 1
• Frédéric Havet
• 2
• Myriam Preissmann
• 3
1. 1.A-SISSaint ÉtienneFrance
2. 2.Projet COATI, I3S (CNRS, UNSA) and INRIASophia AntipolisFrance
3. 3.Univ. Grenoble Alpes and CNRS, G-SCOPGrenobleFrance