Identifying codes of lexicographic product of graphs
  Gravier et al. investigated the identifying codes of Cartesian product of two graphs. In this paper we consider the identifying codes of lexicographic product G[H] of a connected graph G and an arbitrary graph H, and obtain the minimum cardinality of identifying codes of G[H] in terms of some parameters of G and H. 
Min Feng, Min Xu and Kaishun Wang
math.CO