Identifying codes of corona product graphs

For a vertex xx of a graph GG, let NG[x]NG[x] be the set of xx with all of its neighbors in GG. A set CC of vertices is an identifying code   of GG if the sets NG[x]∩CNG[x]∩C are nonempty and distinct for all vertices xx. If GG admits an identifying code, we say that GG is identifiable and denote by γID(G)γID(G) the minimum cardinality of an identifying code of GG. In this paper, we study the identifying code of the corona product H⊙GH⊙G of graphs HH and GG. We first give a necessary and sufficient condition for the corona product H⊙GH⊙G to be identifiable, and then express γID(H⊙G)γID(H⊙G) in terms of γID(G)γID(G) and the (total) domination number of HH. Finally, we compute γID(H⊙G)γID(H⊙G) for some special graphs GG.