Neighbor sum distinguishing total coloring of planar graphs with restrained cycles

Given a graph G = (V (G), E(G)) and a proper total k-coloring mu: V (G) boolean OR E(G) -> {1, 2,..., k}, we call mu neighbor sum distinguishing total coloring provided h(v) not equal h(u) for any uv is an element of E(G) where h(v) = mu(v) + Sigma(uv is an element of E(G)) mu(uv) for any v is an element of V (G). Neighbor sum distinguishing total coloring was first defined by Pilsniak and Wozniak. They conjectured Delta(G) + 3 colors enable any graph G to admit such a coloring. The neighbor sum distinguishing total chromatic number chi(Sigma)'' S is the minimum integer where a graph is needed for this coloring. In this paper, we present two conclusions that chi(Sigma)'' <= Delta(G) + 2 provided there are no 3-cycles adjacent to 4-cycles in a planar graph G with Delta (G) >= 8 without cut edges, and chi(Sigma)'' = <= Delta (G) + 3 provided there are no 4-cycles intersecting with 6-cycles in a planar graph G with Delta (G) >= 7.