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D(β)-vertex-distinguishing total coloring of graphs
作者姓名:ZHANG Zhongfu  LI Jingwen  CHEN Xiang'en  YAO Bing  WANG Wenjie & QIU Pengxiang Institute of Applied Mathematic  Lanzhou Jiaotong University  Lanzhou  China  College of Mathematics and Information Science  Northwest Normal University  Lanzhou  China  College of Information and Electrical Engineering  Lanzhou Jiaotong University  Lanzhou  China
作者单位:ZHANG Zhongfu,LI Jingwen,CHEN Xiang'en,YAO Bing,WANG Wenjie & QIU Pengxiang Institute of Applied Mathematic,Lanzhou Jiaotong University,Lanzhou 730070,China; College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China; College of Information and Electrical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China
摘    要:A new concept of the D(β)-vertex-distinguishing total coloring of graphs, i.e., the proper total coloring such that any two vertices whose distance is not larger thanβhave different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it, is proposed in this paper. The D(2)-vertex-distinguishing total colorings of some special graphs are discussed, meanwhile, a conjecture and an open problem are presented.

关 键 词:graph    total  coloring    D(β)-vertex-distinguishing  total  coloring    D(β)-vertexdistinguishing  total  chromatic  number
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