# Watching systems in graphs: An extension of identifying codes

@article{Auger2013WatchingSI, title={Watching systems in graphs: An extension of identifying codes}, author={David Auger and Ir{\`e}ne Charon and Olivier Hudry and Antoine Lobstein}, journal={Discret. Appl. Math.}, year={2013}, volume={161}, pages={1674-1685} }

## Figures from this paper

## 18 Citations

Random subgraphs make identification affordable

- Mathematics, Computer ScienceArXiv
- 2013

An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code, which is not true for the identifying code number.

Identifying codes and watching systems in Kneser graphs

- MathematicsDiscret. Math. Algorithms Appl.
- 2017

This paper shows that if n ≥ 8, then γID(K(n, 2) = ⌈2n 3 ⌉ if n ≡ 0, 2 (mod 3) and γIDs(N(n) 2) + 1 if n ≤ 4log2 n, which means that in this family of graphs the watching system is more efficient than identifying code.

Fault-tolerant Identifying Codes in Special Classes of Graphs

- Computer ScienceArXiv
- 2021

A fault-tolerant identifying code is introduced called a redundant identifying code, which allows at most one detector to go offline or be removed without disrupting the detection system, and the problem of determining the lowest cardinality of an identifying code for an arbitrary graph is NP-complete.

Watching Systems in the King Grid

- Mathematics, Computer ScienceGraphs Comb.
- 2013

It is proved that in a certain sense when ℓ ≥ 6 the best watching systems in the infinite King grid are trivial, but that this is not the case whenℓ ≤ 4 and that when r is large an asymptotic equivalence of the optimal density of watching systems which is much better than identifying codes’ is given.

Maximum size of a minimum watching system and the graphs achieving the bound

- MathematicsDiscret. Appl. Math.
- 2014

On Graph Identification Problems and the Special Case of Identifying Vertices Using Paths

- MathematicsIWOCA
- 2012

It is shown that any connected graph G has an identifying path cover of size at most \(\left\lceil\frac{2(|V(G)|-1)}{3}\right\rceil\) and the computational complexity of the associated optimization problem is APX-complete.

On the watching number of graphs using discharging procedure

- Mathematics
- 2021

The identifying code has been used to place objects in the sensor and wireless networks. For the vertex x of a graph G, suppose $$N_G[x]$$
is a subset of V(G) containing x and all of its neighbors.…

Combinatorial Algorithms

- MathematicsLecture Notes in Computer Science
- 2012

The relationships between the girth and the quasi-completeness of a graph are established and an upper bound is derived for the largest order γ-quasi-complete subgraph in a graph of minimum degree r is derived.

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