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

摘要

Let chi(t)(Sigma)(G) and chi(it)(Sigma)(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 chi(it)(Sigma)(G) for l-degenerate graphs with integer l = 1, and chi(t)(Sigma)(G) for 2-degenerate graphs, As applications of these results, (i) for a general graph G, chi(t)(Sigma)(G) = chi(i)(Sigma)(t)(G) = max {Delta[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 chi(t)(Sigma)(G) if Delta(G) = 6 and show that chi(t)(Sigma)(G) = 7 if Delta (G) = 5. (C) 2017 Elsevier B.V. All rights reserved.