On generalized neighbor sum distinguishing index of planar graphs

For a proper k-edge coloring phi: E(G) -> {1,2, ..., k} of a graph G, let w(v) denote the sum of the colors taken on the edges incident to the vertex v. Given a positive integer p, the Sigma(p)-neighbor sum distinguishing k-edge coloring of G is phi such that for each edge uv is an element of E(G), vertical bar w(v)- w(u)vertical bar >= p. We denote the smallest integer k in such coloring of G by chi'Sigma p (G). For p = 1, Wang et al. proved that chi'(Sigma p )(G) <= max{Delta(G)+10, 25}. In this paper, we show that, if G is a planar graph without isolated edges, then chi'(Sigma p ) (G) <= max{Delta(G) (16p - 6), f(p)}, where f(p) = max{22p + 3, 8p(2) +26p+1+(2p+1)root 16p(2)+96p-15/4}.