D(β)-vertex-distinguishing total coloring of graphs |
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| Authors: | Zhang Zhongfu Li Jingwen Chen Xiang&#;en Yao Bing Wang Wenjie and Qiu Pengxiang |
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| Institution: | (1) Institute of Applied Mathematic, Lanzhou Jiaotong University, Lanzhou, 730070, China;(2) College of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730070, China;(3) College of Information and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China |
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| Abstract: | 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 than β have 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. |
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| Keywords: | graph total coloring D(β )-vertex-distinguishing total coloring D(β )-vertex-distinguishing total chromatic number |
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