Watching systems in graphs: An extension of identifying codes

  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.},
Random subgraphs make identification affordable
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
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
Fault-tolerant Identifying Codes in Special Classes of Graphs
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
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
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
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.


On graphs having a V\{x} set as an identifying code
Constructing codes identifying sets of vertices
For all t ≥  2, we give an explicit construction of an infinite family of graphs such that G admits a code identifying sets of at most t vertices of G of cardinality O(t2 ln |V(G)|) for all members G
Codes Identifying Sets of Vertices
Two infinite families of optimal (1, ? 2)-identifying codes, which can find malfunctioning processors in a binary hypercube F2n, are provided and Constructions and lower bounds on these codes are given.
Discriminating codes in bipartite graphs
On the identification problems in products of cycles
On the Identification of Vertices and Edges Using Cycles
This work considers the problem of minimizing k when the subgraphs Ci are required to be cycles or closed walks in a graph G, and studies the cases when G is the binary hypercube, or the two-dimensional p-ary space with respect to the Lee metric.
On graphs admitting codes identifying sets of vertices
Let G = (V, E) be a graph and N [X] denote the closed neighbourhood of X ⊆ V , that is to say, the union of X with the set of vertices which are adjacent to X. Given an integer t ≥ 1, a subset of
On a New Class of Codes for Identifying Vertices in Graphs
We investigate a new class of codes for the optimal covering of vertices in an undirected graph G such that any vertex in G can be uniquely identified by examining the vertices that cover it. We
Maximum size of a minimum watching system and the graphs achieving the bound