JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (4): 48-54.doi: 10.6040/j.issn.1671-9352.0.2020.029

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Vertex-distinguishing general-total coloring of K4,4,p

MA Jing-jing, CHEN Xiang-en*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-03-29

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Abstract: The optimal vertex-distinguishing general total coloring of complete tripartite graph K4,4,p is discussed by using of the methods of distributing the color sets in advance, constructing the colorings, contradiction and combinatorial analysis. The vertex-distinguishing general total chromatic number of K4,4,p is determined.

Key words: complete tripartite graph, general total coloring, vertex-distinguishing general total coloring, vertex-distinguishing general total chromatic number

CLC Number: 

  • O157.5
[1] HARARY F, PLANTHOLT M. The point-distinguishing chromatic index[M]. New York: Wiley Interscience, 1985:147-162.
[2] HORNÁK M, SOTÁK R. The fifth jump of the point-distinguishing chromatic index of Kn,n[J]. Ars Combinatoria, 1996, 42:233-242.
[3] HOR(~overN)ÁK M, SOTÁK R. Localization of jumps of the point-distinguishing chromatic index of Kn,n[J]. Discussiones Mathematicae Graph Theory, 1997, 17(2):243-251.
[4] HOR(~overN)ÁK M, ZAGAGLIA S N. On the point-distinguishing chromatic index of Km,n[J]. Ars Combinatoria, 2006, 80:75-85.
[5] ZAGAGLIA S N. On the value of the point-distinguishing chromatic index of Kn,n[J]. Ars Combinatoria, 1990, 29B:235-244.
[6] CHEN X E. Point-distinguishing chromatic index of the union of paths[J]. Czechoslovak Mathematical Journal, 2014, 64(3):629-640.
[7] CHEN X E, GAO Y P, YAO B.Vertex-distinguishing IE-total colorings of complete bipartite graphs Km,n(m[J]. Discussiones Mathematicae, Graph Theory, 2013, 33:289- 306.
[8] LIU C J, ZHU E Q. General vertex-distinguishing total coloring of graphs[J]. Journal of Applied Mathematics, 2014, 2014: 849748.
[9] 陈祥恩,李婷,王治文. 一类含有4-圈的单圈图一般点可区别全染色[J]. 大连理工大学学报, 2017, 57(3):316-320. CHEN Xiangen, LI Ting, WANG Zhiwen. General vertex-distinguishing total colorings of a family of unicyclic graphs including C4[J]. Journal of Dalian University of Technology, 2017, 57(3):316-320.
[10] 寇艳芳,陈祥恩,王治文. K1, 3, p和K1, 4, p的点可区别的IE-全染色及一般全染色[J]. 山东大学学报(理学版), 2018, 53(8):53-60. KOU Yanfang, CHEN Xiangen, WANG Zhiwen. Vertex-distinguishing IE-total coloring and general-total coloring of K1,3,p and K1,4,p[J]. Journal of Shandong University(Natural Science), 2018, 53(8):53-60.
[11] 寇艳芳,陈祥恩,王治文. K1,5,p和K1,6,p的点可区别的IE-全染色及一般全染色[J]. 浙江大学学报(理学版), 2018, 45(5):533-539. KOU Yanfang, CHEN Xiangen, WANG Zhiwen. Vertex-distingnishing IE-total coloring and general-total coloring of K1,5,p and K1,6,P[J]. Journal of Zhejiang University(Science Edition), 2018, 45(5):533-539.
[1] YANG Jia-rui, CHEN Xiang-en. Vertex-distinguishing general total coloring of K3,3,p [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 18-23.
[2] . Vertex-distinguishing IE-total coloring and general-total coloring of K1,3,p and K1,4,p [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 53-60.
[3] LU Shi-fang1, WEI Liang2, ZHAO Hai-xing2. On signless Laplace integral graphs of complete tripartite graphs [J]. J4, 2012, 47(12): 41-46.
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