Combinatorial identification problems and graph powers

This is a summary of the author’s PhD thesis supervised by Pr. Olivier Hudry and defended on 7th June 2010 at Télécom ParisTech. The thesis is written in French (introduction and overview of results) and English (articles, which contain the proofs) and is available from the author upon request or from http://www.lri.fr/~dauger/. It deals in a first part with algorithmic and combinatorial properties of different variations on identifying codes in undirected graphs, a theoretical model for problems of detection and localization in networks. These issues led us to consider a notion of powers of graphs, which we investigate into several directions in a second part.