2009/08/19 by Chunxia Chen, Chen, Chunxia, Changhong Lü +4
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Error Correcting Code Techniques #FOS: Mathematics #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.0908.2750
arxiv created 2009/08/19 · openalex publication_date 2009/08/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V,E) be a graph and let r≥ 1 be an integer. For a set D ⊆ V, define Nr[x] = \y ∈ V: d(x, y) ≤ r\ and Dr(x) = Nr[x] ∩ D, where d(x,y) denotes the number of edges in any shortest path between x and y. D is known as an r-identifying code (r-locating-dominating set, respectively), if for all vertices x∈ V (x ∈ V\backslash D, respectively), Dr(x) are all nonempty and different. In this paper, we provide complete results for r-identifying codes in paths and odd cycles; we also give complete results for 2-locating-dominating sets in cycles.