Several Kinds of Chromatic Numbers of Multi-fan Graphs

Shunqin Liu

doi:doi:10.11648/j.acm.20160503.16

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Several Kinds of Chromatic Numbers of Multi-fan Graphs

Shunqin Liu

Published in Applied and Computational Mathematics (Volume 5, Issue 3)

Received: 10 July 2016 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.

Published in	Applied and Computational Mathematics (Volume 5, Issue 3)
DOI	10.11648/j.acm.20160503.16
Page(s)	133-137
Creative Commons	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), 2016. 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.

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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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ACS 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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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Several Kinds of Chromatic Numbers of Multi-fan Graphs
AU  - Shunqin Liu
Y1  - 2016/07/11
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.16
DO  - 10.11648/j.acm.20160503.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 133
EP  - 137
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160503.16
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.
VL  - 5
IS  - 3
ER  -

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Author Information

Shunqin Liu

School of Information Science & Technology, Xiamen University Tan Kah Kee College, Zhangzhou, China

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APA Style

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

Copy | Download

ACS 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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Several Kinds of Chromatic Numbers of Multi-fan Graphs
AU  - Shunqin Liu
Y1  - 2016/07/11
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160503.16
DO  - 10.11648/j.acm.20160503.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 133
EP  - 137
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160503.16
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.
VL  - 5
IS  - 3
ER  -

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