on the list distinguishing number of graphs

A graph g is said to be k-distinguishable if every vertex of thegraph can be colored from a set of k colors such that no non-trivial auto-morphism xes every color class. the distinguishing number d(g) is theleast integer k for which g is k-distinguishable. a list assignment to g isan assignment l = fl(v)gv2v (g) of lists of labels to the vertices of g. adistinguishing l-labeling of g is a distinguishing labeling of g where thelabel of each vertex v comes from l(v). the list distinguishing number ofg, dl(g) is the minimum k such that every list assignment to g in whichjl(v)j = k for all v 2 v (g) yields a distinguishing l-labeling of g. in thispaper, we study and compute the list-distinguishing number of some familiesof graphs. we also study graphs with the distinguishing number equal thelist distinguishing number.