JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (8): 53-60.doi: 10.6040/j.issn.1671-9352.0.2017.240

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Vertex-distinguishing IE-total coloring and general-total coloring of K1,3,p and K1,4,p

  

  1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China
  • Received:2017-05-18 Online:2018-08-20 Published:2018-07-11

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Abstract: The vertex-distinguishing IE-total coloring and vertex-distinguishing general total coloring of complete tripartite graphs K1,3,p and K1,4,pare discussed by distributing the color sets in advance,constructing the colorings and proving by contradiction. The vertex-distinguishing IE-total chromatic number and vertex-distinguishing general total chromatic number of K1,3,p and K1,4,p have been determined.

Key words: general total coloring, vertex-distinguishing general total coloring, IE-total coloring, complete tripartite graphs, vertex-distinguishing IE-total coloring

CLC Number: 

  • O157.5
[1] HARARY F, PLANTHOLT M. “Conditional colorability in graphs,” in graphs and applications[M]. New York: John Wiley & Sons,1985.
[2] HORNAK M, SOTAK R. The fifth jump of the point-distinguishing chromatic index of Kn,n[J]. Ars Combinatoria, 1996, 42:233-242.
[3] HORNAK M, SOTAK R. Localization jumps of the point-distinguishing chromatic index of Kn,n[J]. Discuss Math Graph Theory, 1997, 17:243-251.
[4] HORNAK M, ZAGAGLIA-SALVI N. On the point-distinguishing chromatic index of Km,n[J]. Ars Combinatoria, 2006, 80:75-85.
[5] ZAGAGLIA-SALVI N. On the value of the point-distinguishing chromatic index of Kn,n[J]. Ars Combinatoria, 1990, 29B:235-244.
[6] CHEN Xiangen. Point-distinguishing chromatic index of the union of paths[J]. Czechoslovak Mathematical Journal, 2014, 64(3):629-640.
[7] CHEN Xiangen, GAO Yuping, YAO Bing. Vertex-distinguishing IE-total colorings of complete bipartite graphs Km,n(m[J]. Discussiones Mathematicae Graph Theory, 2013, 33:289-306.
[8] LIU C, ZHU E. General Vertex-distinguishing total coloring of graphs[J]. Journal of Applied Mathematics, 2014, Article ID 849748, 7 pages.
[1] LU Shi-fang1, WEI Liang2, ZHAO Hai-xing2. On signless Laplace integral graphs of complete tripartite graphs [J]. J4, 2012, 47(12): 41-46.
[2] WANG Guo-xing. Vertex distinguishing IE-total chromatic numbers of mC3 [J]. J4, 2011, 46(2): 57-61.
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