Identifying and locating-dominating codes on chains and cycles

Nathalie Bertrand, Irène Charon, Olivier Hudry, Antoine Lobstein
2004 European journal of combinatorics (Print)  
Consider a connected undirected graph G = (V, E), a subset of vertices C ⊆ V , and an integer r ≥ 1; for any vertex v ∈ V , let B r (v) denote the ball of radius r centered at v, i.e., the set of all vertices within distance r from v. If for all vertices v ∈ V (respectively, v ∈ V \C), the sets B r (v) ∩ C are all nonempty and different, then we call C an r -identifying code (respectively, an r -locating-dominating code). We study the smallest cardinalities or densities of these codes in chains (finite or infinite) and cycles.
doi:10.1016/j.ejc.2003.12.013 fatcat:q3hhk5sjrzeodcr5jpxb3l7h5q