# 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}
}`
• Published 5 May 2010
• Mathematics, Computer Science
• Discret. Appl. Math.
18 Citations
Random subgraphs make identification affordable
• Mathematics, Computer Science
ArXiv
• 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
• Mathematics
Discret. 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.
Identifying path covers in graphs
• Mathematics
J. Discrete Algorithms
• 2013
Fault-tolerant Identifying Codes in Special Classes of Graphs
• Computer Science
ArXiv
• 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 Science
Graphs 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.
On Graph Identification Problems and the Special Case of Identifying Vertices Using Paths
• Mathematics
IWOCA
• 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
• S. Smyth
• Mathematics
Lecture 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.