Identifying codes and locating-dominating sets on paths and cycles

Citations of this article
Mendeley users who have this article in their library.


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\D, respectively), Dr(x) are all nonempty and different. Roberts and Roberts [D.L. Roberts, F.S. Roberts, Locating sensors in paths and cycles: the case of 2-identifying codes, European Journal of Combinatorics 29 (2008) 7282] provided complete results for the paths and cycles when r=2. In this paper, we provide results for a remaining open case in cycles and complete results in paths for r-identifying codes; we also give complete results for 2-locating-dominating sets in cycles, which completes the results of Bertrand et al. [N. Bertrand, I. Charon, O. Hudry, A. Lobstein, Identifying and locatingdominating codes on chains and cycles, European Journal of Combinatorics 25 (2004) 969987]. © 2011 Elsevier B.V. All rights reserved.




Chen, C., Lu, C., & Miao, Z. (2011). Identifying codes and locating-dominating sets on paths and cycles. Discrete Applied Mathematics, 159(15), 1540–1547.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free