Neighbor sum distinguishing total coloring and list neighbor sum distinguishing total coloring

Let χΣt(G) and χΣlt(G) be the neighbor sum distinguishing total chromatic and total choice numbers of a graph G, respectively. In this paper, we present some new upper bounds of χΣlt(G) for ℓ-degenerate graphs with integer ℓ≥1, and of χΣt(G) for 2-degenerate graphs. As applications of these results, (i) for a general graph G, χΣt(G)≤χΣlt(G)≤max{Δ(G)+⌊3col(G)2⌋−1,3col(G)−2}, where col(G) is the coloring number of G; (ii) for a 2-degenerate graph G, we determine the exact value of χΣt(G) if Δ(G)≥6 and show that χΣt(G)≤7 if Δ(G)≤5.