Identifying Codes in Line Graphs

Identifying codes in line graphs

An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We study the edge-identifying code problem, i.e. the identifying code problem in line graphs. If γID(G) denotes the size of a minimum identifying code of an identifiable graph G, we show that the usual bound γID(G) ≥ ⌈log2(n+1)⌉, whe...

Identifying codes in vertex-transitive graphs

We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V |) + 1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that re...

Possible cardinalities for identifying codes in graphs

Identifying Codes in Vertex-Transitive Graphs and Strongly Regular Graphs

We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V |) + 1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that re...

Identifying Codes on Directed De Bruijn Graphs

For a directed graph G, a t-identifying code is a subset S ⊆ V (G) with the property that for each vertex v ∈ V (G) the set of vertices of S reachable from v by a directed path of length at most t is both non-empty and unique. A graph is called t-identifiable if there exists a t-identifying code. This paper shows that the de Bruijn graph ~ B(d, n) is 1and 2-identifiable and examines conditions ...