Equitable neighbour-sum-distinguishing edge and total colourings

We study in this paper equitable neighbour-sum-distinguishing edge colourings and total colourings, that is colourings γ for which the number of elements in any two colour classes of γ differ by at most one. We determine the equitable neighbour-sum-distinguishing index of complete graphs, complete bipartite graphs and forests, and the equitable neighbour-sum-distinguishing total chromatic number of complete graphs and bipartite graphs.