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

作者：Lu, You; Han, Miaomiao; Luo, Rong^*

来源：Discrete Applied Mathematics, 2018, 237: 109-115.

DOI：10.1016/j.dam.2017.12.001

• Neighbor sum distinguishing total coloring
• l-degenerate
• Coloring number
• Maximum degree

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.

• 出版日期2018-3-11
• 单位江苏师范大学; 西北工业大学