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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 54-60.doi: 10.6040/j.issn.1671-9352.0.2020.592

• • 上一篇    

m个长为14的圈的不交并的点可区别Ⅰ-全染色

赵亚迪,陈祥恩*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2022-06-10
  • 作者简介:赵亚迪(1997— ),女,硕士研究生,研究方向为图论及其应用. E-mail:aady19970228@163.com*通信作者简介:陈祥恩(1965— ),男,教授,研究方向为图论及其应用. E-mail:chenxe@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11761064,61163037)

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

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,证明mC14的最优点可区别Ⅰ-全染色及最优点可区别Ⅵ-全染色,确定图mC14的点可区别Ⅰ-全色数和点可区别Ⅵ-全色数。结论表明,点可区别Ⅰ-全染色猜想和点可区别Ⅵ-全染色猜想对图mC14成立。

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

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

中图分类号: 

  • O157.5
[1] BURRIS A C. Vertex-distinguishing edge-coloring[D]. Memphis: Memphis State University, 1993.
[2] BURRIS A C, SCHELP R H. Vertex-distinguishing proper edge-coloring[J]. J Graph Theory, 1997, 26:73-82.
[3] CERNY J,HORÑÁK M, SOTÁK R. Observability of a graphs[J]. Math Slovaca, 1996, 46:21-31.
[4] BALISTER P N, RIORDAN O M, SCHELP R H. Vertex-distinguishing edge colorings of graphs[J]. J Graph Theory, 2003, 42:95-109.
[5] HARARY F, PLANTHOLT M. The point-distinguishing chromatic index[M] //HARARY F, MAYBEE J S. Graphs and Application. New York: Wiley Interscience, 1985: 147-162.
[6] HORNÁK M, ZAGAGLIA SALVI N. On the point-distinguishing chromatic index of complete bipartite graphs[J]. ARS Combinatoria, 2006, 80:75-85.
[7] ZHANG Z F, QIU P X, XU B G, et al. Vertex-distinguishing total colorings of graphs[J]. ARS Combinatoria, 2008, 87:33-45.
[8] 陈祥恩. 图的可区别染色引论[M]. 北京: 中国科学技术出版社, 2015: 108-141. CHEN Xiangen. An introduction to distinguishing colorings of graphs[M]. Beijing: Science and Technology of China Press, 2015: 108-141.
[9] CHEN X E, LI Z P. Vertex-distinguishing Ⅰ-total colorings of graphs[J]. Utilitas Mathematica, 2014, 95:319-327.
[10] CHEN X E, GAO Y P, YAO B. Not necessarity proper total colorings which are adjacent vertex distinguishing[J]. International Journal of Computer Mathematics, 2013, 90(11):2298-2307.
[11] 苗婷婷, 陈祥恩, 王治文. 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(自然科学版), 2017, 57(4):430-453. MIAO Tingting, CHEN Xiangen, WANG Zhiwen. Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of join-graph of cycle and path[J]. Journal of Dalian University of Technology, 2017, 57(4):430-453.
[12] 苗婷婷, 陈祥恩, 王治文. Cm∨Cn, Cm∨Wn, Cm∨Fn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. MIAO Tingting, CHEN Xiangen, WANG Zhiwen.Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of Cm∨Cn, Cm∨Wn, Cm∨Fn[J]. Journal of Xiamen University(Natural Science), 2017, 56(6):870-875.
[13] 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. YANG Han, CHEN Xiangen.Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of mC4[J]. Journal of Xiamen University(Natural Science), 2020, 59(1):85-89.
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