JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (11): 76-82.doi: 10.6040/j.issn.1671-9352.0.2020.362

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Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of mC7

YANG Han, CHEN Xiang-en*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-11-15

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Abstract: By using the methods of constructing a matrix which was composed of color sets and empty set as the elements, distributing color sets in advance and coloring explicitly, to give the optimal vertex distinguishing Ⅰ-total colorings and the optimal vertex distinguishing Ⅵ-total colorings of mC7. Thus vertex distinguishing Ⅰ-total chromatic numbers and the vertex distinguishing Ⅵ-total chromatic numbers of mC7 are determined. The results show that the VDITC conjecture and VDVITC conjecture are valid for mC7.

Key words: cycle, disjoint union, vertex-distinguishing Ⅰ-total coloring, vertex-distinguishing Ⅵ-total coloring, vertex-distinguishing Ⅰ-total chromatic number, vertex-distinguishing Ⅵ-total chromatic number

CLC Number: 

  • O157.5
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