On identification in the triangular grid
Journal of Combinatorial Theory Series B
A linear algorithm for minimum 1-identifying codes in oriented trees
Discrete Applied Mathematics
On locating-dominating sets in infinite grids
European Journal of Combinatorics
Joint Monitoring and Routing in Wireless Sensor Networks Using Robust Identifying Codes
Mobile Networks and Applications
Identifying path covers in graphs
Journal of Discrete Algorithms
| Hi-index | 754.84 |
Let G=(V, A) be a directed, asymmetric graph and C a subset of vertices, and let Br-(v) denote the set of all vertices x such that there exists a directed path from x to v with at most r arcs. If the sets Br-(v) ∩ C, v ∈ V (respectively, v ∈ V/C), are all nonempty and different, we call C an r-identifying code (respectively, an r-locating-dominating code) of G. In other words, if C is an r-identifying code, then one can uniquely identify a vertex v ∈ V only by knowing which codewords belong to Br-(v), and if C is r-locating-dominating, the same is true for the vertices v in V/C. We prove that, given a directed, asymmetric graph G and an integer k, the decision problem of the existence of an r-identifying code, or of an r-locating-dominating code, of size at most k in G, is NP-complete for any r≥1 and remains so even when restricted to strongly connected, directed, asymmetric, bipartite graphs or to directed, asymmetric, bipartite graphs without directed cycles.