%0 Journal Article
%T Halin图的邻和可区别全染色<br>Neighbor sum distinguishing total coloring of Halin graph
%A 宋红杰
%A 巩相男
%A 潘文华
%A 徐常青&lt
%A br&gt
%A SONG Hong-jie
%A GONG Xiang-nan
%A PAN Wen-hua
%A XU Chang-qing
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2015.300
%X 摘要： 令［k］={1,2,…,k}, φ为图G的一个正常［k］-全染色。用f(v)表示点v及所有与其关联的边的颜色的加和,如果对任意边uv∈E(G),有f(u)≠f(v),则称该染色为图G的［k］-邻和可区别全染色。k的最小值称为图G的邻和可区别全色数,记为χ″Σ(G)。Pilsniak和Wozniak提出猜想:对任意简单图G,有χ″Σ(G)≤Δ(G)+3,其中Δ(G)表示图G的最大度。运用组合零点定理证明了该猜想对于任一Halin图成立。<br>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
%K 邻和可区别全染色
%K Halin图
%K 组合零点定理
%K &lt
%K br&gt
%K Halin graph
%K combinatorial nullstellensatz
%K neighbor sum distinguishing total coloring
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.300