%0 Journal Article
%T 最大度为3或4的图的邻和可区别全染色<br>Neighbor sum distinguishing total coloring of graphs with maximum degree 3 or 4
%A 姚京京
%A 徐常青&lt
%A br&gt
%A YAO Jing-jing
%A XU Chang-qing
%J 山东大学学报（理学版）
%D 2015
%R 10.6040/j.issn.1671-9352.0.2014.362
%X 摘要： 图G的一个正常[k]-全染色是一个映射φ:V∪E→｛1,2,…,k｝,使得V∪E中任意一对相邻或者相关联元素染不同颜色.用f(v)表示点v及所有与其关联的边的颜色的加和,若对任意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的最小值称作图G的邻和可区别全色数,记为tndiΣ(G).<br>Abstract: A proper [k]-total coloring of a graph G is a map φ:V∪E→｛1,2,…,k｝ such that φ(x)≠φ(y) for each pair of adjacent or incident elements x,y∈V∪E. 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 tndiΣ(G) denote the smallest value k in such a coloring of G. Pil?niak and Wo?niak first introduced this coloring and conjectured that tndiΣ(G)≤Δ(G)+3 for any simple graph with maximum degree Δ(G). The maximum average degree of G is the maximum of the average degree of its non-empty subgraphs, which is denoted by mad(G). By using the Combinatorial Nullstellensatz and the discharging method, it is proved that if G is a graph with Δ(G)=3 and mad(G)<125, or Δ(G)=4 and mad(G)<52, then tndiΣ(G)≤Δ(G)+2
%K 邻和可区别全染色
%K 最大平均度
%K 组合零点定理
%K &lt
%K br&gt
%K neighbor sum distinguishing total coloring
%K maximum average degree
%K Combinatorial Nullstellensatz
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2014.362