JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (6): 54-60.doi: 10.6040/j.issn.1671-9352.0.2020.592

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Vertex-distinguishing Ⅰ-total colorings of mC14

ZHAO Ya-di, CHEN Xiang-en*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-06-10

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Abstract: The problems of the optimal vertex-distinguishing Ⅰ-total colorings(VDITC)and the optimal vertex-distinguishing Ⅵ-total colorings(VDVITC)of graph mC14 are proved by constructing a matrix which is composed of color sets and empty set as the elements and using the methods of distributing color sets in advance and describing coloring explicitly. Thus vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC14 are determined. The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC14.

Key words: 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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