JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 29-35.doi: 10.6040/j.issn.1671-9352.0.2022.667

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Vertex distinguishing general total colorings of complete 3-partite graphs by multisets

Yongjun WANG(),Xiang CHEN*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-12-21 Online:2024-06-20 Published:2024-06-17
  • Contact: Xiang CHEN E-mail:wangyongjun0612@163.com;chenxe@nwnu.edu.cn

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Abstract:

In this paper, we use the method of contradiction, constructing concrete coloring and distributing the color sets in advance, discuss the general total colorings of complete 3-partite graph which are vertex-distinguished by multisets. Torresponding optimal coloring and the chromatic numbers of the corresponding colorings are obtained.

Key words: complete 3-partite graph, general total coloring, multiset, color set, distinguishing

CLC Number: 

  • O157.5
1 HARARY F, PLANTHOLT M. The point-distinguishing chromatic index[M]//Graphs and Application. New York: Wiley, 1985: 147-162.
2 LIUC J,ZHUE Q.General vertex-distinguishing total coloring of graphs[J].Journal of Applied Mathematics,2014,2014,1-7.
3 陈祥恩,苏丽,王治文.完全二部图K2, n和K3, n的一般点可区别全染色[J].吉林大学学报(理学版),2016,54(6):1289-1293.
CHENXiang'en,SULi,WANGZhiwen.General vertex-distinguishing total colorings of complete bipartite graph K2, n and K3, n[J].Journal of Jilin University(Science Edition),2016,54(6):1289-1293.
4 陈祥恩,张爽.图K2, 3, p的点可区别IE-全染色及一般全染色[J].西北师范大学学报(自然科学版),2020,56(3):7-13, 30.
CHENXiang'en,ZHANGShuang.Vertex-distinguishing IE-total coloring and general total of graph K2, 3, p[J].Journal of Northwest Normal University(Natural Science),2020,56(3):7-13, 30.
5 陈祥恩,王勇军.完全二部图的点被多重集可区别的IE-全染色及一般全染色[J].吉林大学学报(理学版),2022,60(4):838-844.
CHENXiang'en,WANGYongjun.IE-total coloring and general total coloring of complete bipartite graphs vertex-distinguished by multiple set[J].Journal of Jilin University(Science Edition),2022,60(4):838-844.
6 邵嘉裕.组合数学[M].上海:同济大学出版社,1990.
SHAOJiayu.Combinatorial mathematics[M].Shanghai: Tongji University Press,1990.
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