Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard
Theoretical Computer Science
On cages admitting identifying codes
European Journal of Combinatorics
Graph Theory
A linear algorithm for minimum 1-identifying codes in oriented trees
Discrete Applied Mathematics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
On the size of identifying codes in triangle-free graphs
Discrete Applied Mathematics
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Let G be a finite undirected graph with vertex set V(G). If v@?V(G), let N[v] denote the closed neighbourhood of v, i.e. v itself and all its adjacent vertices in G. An identifying code in G is a subset C of V(G) such that the sets N[v]@?C are nonempty and pairwise distinct for each vertex v@?V(G). We consider the problem of finding the minimum size of an identifying code in a given graph, which is known to be NP-hard. We give a linear algorithm that solves it in the class of trees, but show that the problem remains NP-hard in the class of planar graphs with arbitrarily large girth.