Applied and Computational Mathematics

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Several Kinds of Chromatic Numbers of Multi-fan Graphs

Received: 10 July 2016    Accepted:     Published: 11 July 2016
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Abstract

Coloring problem is a classical difficult problem of graph theory. It is a fundamental problem in scientific computation and engineering design. In recent years, a variety of graph coloring problems frequently appeared and solved many problems in production. It is a difficult problem to discuss the chromatic number of a given graph class. In the paper, we introduce several kinds of chromatic numbers of graphs such as adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing edge chromatic number, and the multi-fan graphs are considered.

DOI 10.11648/j.acm.20160503.16
Published in Applied and Computational Mathematics (Volume 5, Issue 3, June 2016)
Page(s) 133-137
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Multi-fan Graphs, Adjacent-vertex-distinguishing Total Chromatic Number, Adjacent-vertex-distinguishing Proper Edge Chromatic Number, Smarandachely-adjacent-vertex-distinguishing Edge Chromatic Number

References
[1] Chen Xiang-en, Zhang Zhong-fu, “Adjacent-Vertex-Distinguishing Total Chromatic Number of ,” Journal of Mathematical Reserch and Exposition, Dalian. vol. A26, pp. 489-494, August 2015.
[2] Liu Hua, Ye Jian-hua, “Adjacent Vertex-Distinguishing Edges Coloring of ()” Journal of East China Jiaotong University. vol 24. pp. 157-158, October 2007.
[3] Liu Shun-qin, Chen Xiang-en. “Smarandachely Adjacent-vert -ex-distinguishing Proper Edge Coloring of ”. Journal of Lanzhou University of Technology. vol. 41. pp. 155-158, August 2015.
[4] Zhang Dong-han, Zhang Zhong-fu. “The Upper Bound of the Adjacent Vertex Strongly Distinguishing Total Chromatic Number of the Graph”. Advances in Mathematics. vol. 40 pp. 168-172. April 2011.
[5] Qiang Hui-ying, Li Mu-chun. “A Bound on Vertex Distinguishing Total Coloring of Graphs with Distance Constrant for Recurrent Event Data”. Acta Mathematicae Applicatae Sinica. vol. 34. pp. 554-559. May 2011.
[6] Tian Jing-jing, Deng Fang-an. “Adjacent Vertex-distinguishing VE-Total Chromatic Number of the Crown Graph and ”. Mathematics in Practice and Theory. vol. 41. pp. 189-192. August. 2011.
[7] Yao Bing, Cheng Hui. “Behaviors of Vertex Neighbors of Trees Under Some Graph Coloring”. AclaMathematica Scientia. vol. 31. pp. 567-576. May 2011
[8] Wen Fei, Wang Zhi-wen. “Vertex –distinguishing Total Coloring of Some Complement Double Graphs’. Journal of Shandong University (Natural Science). vol. 46. pp. 45-50 February 2011.
[9] Chen Xiang-en, Ma Yan-rong. “Adjacent-Vertex-Distingui -shing Total Chromatic Number of ”. Journal of Jilin University (Science Edition). vol. 49. pp. 68-70. January 2011.
[10] Tian Jing-jing. “The Smarandachely Adjacent –Vertex –Eege Coloring of Some Mycielski’s Graph”. Journal of Math(PRC). vol. 32. pp. 723-728. April 2012.
[11] Zhang Zhong-fu, Chen Xiang-en, Li Jing-wen. “On adjacent –vertex-distinguishing total coloring of graphs.” Sci.China. Ser vol. 48. pp. 289-299. June 1997.
[12] Li Jing-wen, Xu Ban-gen, Li Mu-chun. “On the vertex-distinguishing chromatic number of ” Journal of Shan Dong University (Nature Science ). vol. 43. pp. 24-30 August 2008.
Author Information
  • School of Information Science & Technology, Xiamen University Tan Kah Kee College, Zhangzhou, China

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    Shunqin Liu. (2016). Several Kinds of Chromatic Numbers of Multi-fan Graphs. Applied and Computational Mathematics, 5(3), 133-137. https://doi.org/10.11648/j.acm.20160503.16

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    Shunqin Liu. Several Kinds of Chromatic Numbers of Multi-fan Graphs. Appl. Comput. Math. 2016, 5(3), 133-137. doi: 10.11648/j.acm.20160503.16

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    AMA Style

    Shunqin Liu. Several Kinds of Chromatic Numbers of Multi-fan Graphs. Appl Comput Math. 2016;5(3):133-137. doi: 10.11648/j.acm.20160503.16

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  • @article{10.11648/j.acm.20160503.16,
      author = {Shunqin Liu},
      title = {Several Kinds of Chromatic Numbers of Multi-fan Graphs},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {3},
      pages = {133-137},
      doi = {10.11648/j.acm.20160503.16},
      url = {https://doi.org/10.11648/j.acm.20160503.16},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20160503.16},
      abstract = {Coloring problem is a classical difficult problem of graph theory. It is a fundamental problem in scientific computation and engineering design. In recent years, a variety of graph coloring problems frequently appeared and solved many problems in production. It is a difficult problem to discuss the chromatic number of a given graph class. In the paper, we introduce several kinds of chromatic numbers of graphs such as adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing edge chromatic number, and the multi-fan graphs are considered.},
     year = {2016}
    }
    

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    AB  - Coloring problem is a classical difficult problem of graph theory. It is a fundamental problem in scientific computation and engineering design. In recent years, a variety of graph coloring problems frequently appeared and solved many problems in production. It is a difficult problem to discuss the chromatic number of a given graph class. In the paper, we introduce several kinds of chromatic numbers of graphs such as adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing edge chromatic number, and the multi-fan graphs are considered.
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