mC7的点被多重色集合可区别的I-全染色和VI-全染色
I-Total Coloring and VI-Total Coloring of mC7 Which Are Vertex-Distinguishing by Multiple Sets
DOI: 10.12677/PM.2023.135141, PDF,   
作者: 王娜娜：西北师范大学数学与统计学院，甘肃 兰州
关键词: mC7；I-全染色；VI-全染色；多重集；色集合；点可区别；mC7； I-Total Coloring； VI-Total Coloring； Multiset； Color Set； Vertex-Distinguishing
摘要: 通过构造以多重色集合和空集为元素的矩阵，应用组合分析法及构造具体染色的方法，得到了mC7的点被多重色集合可区别的I-全染色和VI-全染色的全色数及最优染色方案。
Abstract: By use of the method of constructing a matrix whose entries are the suitable multiple sets or empty sets and the method of distributing color set in advance, we will give the optimal I-(VI-) total col-orings of mC7 which are vertex­distinguished by multiple sets in this paper. Thereby, we obtain I-(VI-) total chromatic numbers of mC7 which are vertex-distinguished by multiple sets.
文章引用：王娜娜. mC7的点被多重色集合可区别的I-全染色和VI-全染色[J]. 理论数学, 2023, 13(5): 1381-1388. https://doi.org/10.12677/PM.2023.135141

参考文献

[1] Zhang, Z.F., Qiu, P.X., Xu, B.G., et al. (2008) Vertex-Distinguishing Total Coloring of Graphs. Ars Combinatoria, 87, 33-45.
[2] Chen, X.E. and Li, Z.P. (2014) Vertex-Distinguishing I-Total Colorings of Graphs. Utilitas Mathematica, 95, 319-327.
[3] Liu, C.J. and Zhu, E.Q. (2014) General Vertex-Distinguishing Total Coloring of Graphs. Journal of Applied Mathematics, 2014, Article ID: 849748. [Google Scholar] [CrossRef] 
[4] Horňák, M. and Soták, R. (1996) The Fifth Jump of the Point-Distinguishing Chromatic Index of . Ars Combinatoria, 42, 233-242.
[5] Horňák, M. and Soták, R. (1997) Localization of Jumps of the Point-Distinguishing Chromatic Index of . Discussiones Mathematicae Graph Theory, 17, 243-251. [Google Scholar] [CrossRef] 
[6] Horňák, M. and Salvi, N.Z. (2006) On the Point-Distinguishing Chromatic Index of Complete Bipartite Graphs. Ars Combinatoria, 80, 75-85.
[7] Salvi, N.Z. (1990) On the Value of the Point-Distinguishing Chromatic Index of . Ars Combinatoria, 29B, 235-244.
[8] 陈祥恩, 苗婷婷, 王治文. 两条路的联图的点可区别I-全染色[J]. 山东大学学报(理学版), 2017, 52(4): 30-33.
[9] 苗婷婷, 王治文, 陈祥恩. 圈与路联图点可区别I-全染色和点可区别VI-全染色[J]. 大连理工大学学报, 2017, 57(4): 430-435.
[10] 苗婷婷, 王治文, 陈祥恩. 的点可区别I-全染色和点可区别VI-全染色[J]. 厦门大学学报(自然科学版), 2017, 56(6): 870-875.
[11] 杨晗, 陈祥恩. m个阶为4的圈的不交并的点可区别I-全染色和VI-全染色[J]. 厦门大学学报(自然科学版), 2020, 59(1): 85-89.
[12] 赵亚迪, 陈祥恩. 图 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.
[13] Zhang, Z.F., Qiu, P.X., Xu, B.G., et al. (2008) Vertex-Distinguishing Total Coloring of Graphs. Ars Combinatoria, 87, 33-45.
[14] Chen, X.E. and Li, Z.P. (2014) Vertex-Distinguishing I-Total Colorings of Graphs. Utilitas Mathematica, 95, 319-327.
[15] Liu, C.J. and Zhu, E.Q. (2014) General Vertex-Distinguishing Total Coloring of Graphs. Journal of Applied Mathematics, 2014, Article ID: 849748. [Google Scholar] [CrossRef] 
[16] Horňák, M. and Soták, R. (1996) The Fifth Jump of the Point-Distinguishing Chromatic Index of . Ars Combinatoria, 42, 233-242.
[17] Horňák, M. and Soták, R. (1997) Localization of Jumps of the Point-Distinguishing Chromatic Index of . Discussiones Mathematicae Graph Theory, 17, 243-251. [Google Scholar] [CrossRef] 
[18] Horňák, M. and Salvi, N.Z. (2006) On the Point-Distinguishing Chromatic Index of Complete Bipartite Graphs. Ars Combinatoria, 80, 75-85.
[19] Salvi, N.Z. (1990) On the Value of the Point-Distinguishing Chromatic Index of . Ars Combinatoria, 29B, 235-244.
[20] 陈祥恩, 苗婷婷, 王治文. 两条路的联图的点可区别I-全染色[J]. 山东大学学报(理学版), 2017, 52(4): 30-33.
[21] 苗婷婷, 王治文, 陈祥恩. 圈与路联图点可区别I-全染色和点可区别VI-全染色[J]. 大连理工大学学报, 2017, 57(4): 430-435.
[22] 苗婷婷, 王治文, 陈祥恩. 的点可区别I-全染色和点可区别VI-全染色[J]. 厦门大学学报(自然科学版), 2017, 56(6): 870-875.
[23] 杨晗, 陈祥恩. m个阶为4的圈的不交并的点可区别I-全染色和VI-全染色[J]. 厦门大学学报(自然科学版), 2020, 59(1): 85-89.
[24] 赵亚迪, 陈祥恩. 图 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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