the identifying code number and functigraphs

Let g = (v(g),e(g)) be a simple graph. a set d of vertices g is an identifying code of g, if for every two vertices x and y the sets ng[x] d and ng[y]d are non-empty and different. the minimum cardinality of an identifying code in graph g is the identifying code number of g and it is denoted by γid(g). two vertices x and y are twin, when ng[x] = ng[y]. graphs with at least two twin vertices are not identifiable graphs. in this paper, we deal with identifying code number of functigraph of g. two upper bounds on identifying code number of functigraph are given. also, we present some graph g with identifying code number v (g)2.