| mC7的点可区别Ⅰ-全染色和Ⅵ-全染色 |
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| 引用本文： | 杨晗,陈祥恩.mC7的点可区别Ⅰ-全染色和Ⅵ-全染色[J].山东大学学报(理学版),2021,56(11):76-82. |
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| 作者姓名： | 杨晗 陈祥恩 |
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| 作者单位： | 西北师范大学数学与统计学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目(11761064) |
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| 摘 要： | 利用色集合事先分配法及具体的染色给出了mC7的最优点可区别Ⅰ-全染色以及最优点可区别Ⅵ-全染色,进而确定了图mC7的点可区别Ⅰ-全色数及点可区别Ⅵ-全色数。结论表明VDITC猜想和VDVITC猜想对图mC7成立。
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| 关 键 词： | 圈 不交并 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 |
Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of mC7 |
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| YANG Han,CHEN Xiang-en.Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of mC7[J].Journal of Shandong University,2021,56(11):76-82. |
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| Authors: | YANG Han CHEN Xiang-en |
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| Institution: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China |
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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. |
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| Keywords: | 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 |
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