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.
Multi-fan Graphs, Adjacent-vertex-distinguishing Total Chromatic Number, Adjacent-vertex-distinguishing Proper Edge Chromatic Number, Smarandachely-adjacent-vertex-distinguishing Edge Chromatic Number
To cite this article
Several Kinds of Chromatic Numbers of Multi-fan Graphs, Applied and Computational Mathematics.
Vol. 5, No. 3,
2016, pp. 133-137.
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.
Liu Hua, Ye Jian-hua, “Adjacent Vertex-Distinguishing Edges Coloring of ()” Journal of East China Jiaotong University. vol 24. pp. 157-158, October 2007.
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.
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.
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.
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.
Yao Bing, Cheng Hui. “Behaviors of Vertex Neighbors of Trees Under Some Graph Coloring”. AclaMathematica Scientia. vol. 31. pp. 567-576. May 2011
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.
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.
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.
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.
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.