Locating sensors in paths and cycles: The case of 2-identifying codes

For a graph G and a set D V (G), define Nr[x] = {xi V (G) : d(x, xi) r} (where d(x, y) is graph theoretic distance) and Dr(x) = Nr[x] D. D is known as an r-identifying code if for every vertex x, Dr(x) = , and for every pair of vertices x and y, x = y Dr(x) = Dr(y). The various applications of these codes include attack sensor placement in networks and fault detection/localization in multiprocessor or distributed systems. Bertrand et al. [2] and Gravier et al. [16] provide partial results about the minimum size of D for r-identifying codes for paths and cycles and present complete closed form solutions for the case r = 1, based in part on Daniel [14]. We provide complete solutions for the case r = 2.

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: David L. Roberts, Fred S. Roberts
• Keywords: EJC 2008, Et Al, Graph Theoretic Distance, Information Technology, R-identifying Codes