关键词: 邻和可区别全染色, Halin图, 组合零点定理

Abstract: Let ［k］={1,2,…,k}, a mapping φ is a proper ［k］-total coloring of a graph G. Let f(v) denote the sum of the color of vertex v and the colors of the edges incident with v. A ［k］-neighbor sum distinguishing total coloring of G is a ［k］-total coloring of G such that for each edge uv∈E(G), f(u)≠f(v). Let χ″_Σ(G) denote the smallest value k in such a coloring of G. Pilsniak and Wozniak conjectured that χ″_Σ(G)≤Δ(G)+3 for any simple graph with maximum degree Δ(G). By using the Combinatorial Nullstellensatz, it shows that the conjecture holds for any Halin graph.

Key words: Halin graph, combinatorial nullstellensatz, neighbor sum distinguishing total coloring