Neighbor sum distinguishing total chromatic number of planar graphs without, 4-cycles

Let phi be a proper k-total coloring of G = (V (G), E(G)) by using the color set {1, 2,..., k}. For any v is an element of V (G), let f (v) = Sigma(uv is an element of E(G)) phi(uv) + phi(v). The coloring phi is neighbor sum distinguishing if f (u) not equal f (v) for each edge uv is an element of E(G). The neighbor sum distinguishing total chromatic number is the smallest number k in such a coloring of G and denoted by x"(Sigma)(G). In this paper, we determine x"(Sigma)(G) for any planar graph G without 4-cycles and Delta(G) >= 9.