| 图mC15的点可区别Ⅰ-全染色和Ⅵ-全染色 |
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| 引用本文： | 赵亚迪,陈祥恩.图mC15的点可区别Ⅰ-全染色和Ⅵ-全染色[J].吉林大学学报(理学版),2021,59(3):497-512. |
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| 作者姓名： | 赵亚迪 陈祥恩 |
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| 作者单位： | 西北师范大学 数学与统计学院, 兰州 730070 |
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| 摘 要： | 通过构造以色集合和空集为元素的矩阵, 利用色集合事先分配法及构造具体染色的方法, 解决了图mC15的最优点可区别Ⅰ-全染色及最优点可区别Ⅵ-全染色问题, 得到了图mC15的点可区别Ⅰ-全色数和点可区别Ⅵ-全色数. 结果表明, 点可区别Ⅰ-全染色猜想和点可区别Ⅵ-全染色猜想对图mC15成立.
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| 关 键 词： | 点可区别Ⅰ-全染色 点可区别Ⅵ-全染色 点可区别Ⅰ-全色数 点可区别Ⅵ-全色数 |
| 收稿时间： | 2020-10-30 |
Vertex-Distinguishing Ⅰ-Total Colorings and Vertex-Distinguishing Ⅵ-Total Colorings of Graph mC15 |
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| ZHAO Yadi,CHEN Xiang'en.Vertex-Distinguishing Ⅰ-Total Colorings and Vertex-Distinguishing Ⅵ-Total Colorings of Graph mC15[J].Journal of Jilin University: Sci Ed,2021,59(3):497-512. |
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| Authors: | ZHAO Yadi CHEN Xiang'en |
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| Institution: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China |
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| Abstract: | We solved the problems of the optimal vertex-distinguishing Ⅰ-total colorings (VDITC) and the optimal vertex-distinguishing Ⅵ-total colorings (VDVITC) of graph mC15 by constructing a matrix with color sets and empty set as its elements, and using the methods of distributing color sets in advance and describing coloring explicitly, and obtained vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC15. The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC15. |
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| Keywords: | vertex-distinguishing Ⅰ-total colorings vertex-distinguishing Ⅵ-total colorings vertex-distinguishing Ⅰ-total chromatic numbers vertex-distinguishing Ⅵ-total chromatic numbers |
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