According to different conditions, researchers have defined a great deal of coloring problems and the corresponding chromatic numbers. Such as, adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper total chromatic number. And we focus on the smarandachely adjacent-vertex-distinguishing proper edge chromatic number in this paper, study the smarandachely adjacent-vertex-distinguishing proper edge chromatic number of joint graph Cm∨Kn.
Published in | Applied and Computational Mathematics (Volume 5, Issue 5) |
DOI | 10.11648/j.acm.20160505.13 |
Page(s) | 202-206 |
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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. |
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Copyright © The Author(s), 2016. Published by Science Publishing Group |
Graph Theory, Joint Graph, Smarandachely Adjacent-Vertex-Distinguishing Proper Edge Chromatic Number
[1] | Liu Shun-qin, Chen Xiang-en. “Smarandachely Adjacent-Vertex-distinguishing proper edge coloring of ”. vol.41, pp. 155-158. August. 2015. |
[2] | Bondy. J .A. MURTY U S R. Graph Theory. London. Springer.2008. |
[3] | 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. |
[4] | Chen Xiang-en, Zhan-fu, “Adjacent-Vertex-Distinguishing Total Chromatic Number of Pm×Kn,” Journal of Mathematical Research and Exposition, Dalian. vol. A26, pp. 489-494. August. 2015. |
[5] | Liu Shun-qin, Chen Xiang-en. “Smarandachely Adjacent-Vertex-distinguishing proper edge coloring of ”. vol.37,pp.139-145.April.2011. |
[6] | Tian Jing-jing. “The Smarandachely Adjacent –Vertex –Eege Coloring of Some Mycielski’s Graph”. J. of. Math (PRC). vol. 32. pp. 723-728. April 2012. |
[7] | 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. |
[8] | Tian Jing-jing, Deng Fang-an. “Adjacent Vertex-Distinguishing VE-Total Chromatic Number of the Crown Graph Cm.Fn and Cm.Cn”.Mathematics in Practice and Theory. vol. 41. pp. 189-192. August. 2011. |
[9] | Tian Jing-jing. “The Smarandachely Adjacent –Vertex –Eege Coloring of Some Mycielski’s Graph”. J. of. Math(PRC). vol. 32. pp. 723-728. April 2012. |
[10] | Lin Sun, Xiaohan Cheng, Jianliang Wu. “The Adjacent Vertex Distinguishing Total Coloring of Planar Graphs without Adjacent 4-cycles” J. Comb. Optim. DOI 10.1007/S10878-016-0004-1.11 March.2016. |
[11] | Xiaohan Cheng, Guanghui Wang, Jianliang Wu. “The Adjacent Vertex Distinguishing Total Chromatic Numbers of Planar Graphs with △=10” J. Comb. Optim. DOI. 1007/S10878-016-9995-x.04 February.2016. |
[12] | Huijuan Wang, Bin Liu, Yan Gu, Xin Zhang.“Total Coloring of Planar Graphs without Adjacent short cycles” J. Comb. Optim. DOI.1007/S10878-015-9954-y.16. September. 2015. |
[13] | Liu Hua, Feng Jianhua, Ma Shaoxian.”Adjacent Vertex-Distinguishing Edges coloring of Sm . Sn” Journal of East China Jiao-tong University. vol. 24. pp. 157-158. October. 2007. |
[14] | Zhang Donghan, Zhang Zhongfu. “The Upper Bound of Adjacent Vertex Strongly Distinguishing Total Chromatic Number of the Graph”. Advances of Mathematics. vol. 40. No. 2. pp. 168-172. April. 2011. |
[15] | Zhang Z F, Liu L Z, Wang J F. “Adjacent strong edge coloring of graphs”. Appl Math Lett. vol. 15. pp. 623-626. April. 2002. |
[16] | Shunqin Liu. “Several Kinds of Chromatic Numbers of Multi-fan Graphs”. Applied and Computational Mathematics. vol. 5. No. 3. pp. 133-137. June. 2016. |
[17] | Wang YQ, Sun Q, Tao X, Shen L.”Plane graphs with maximum degree 7 and without 5-cycles with chords are 8-totally-colorable. Sci. China A. vol. 41. pp. 95-104. February. 2011. |
[18] | Wang B, Wu JL, Wang HJ. “Total coloring of planar graphs without chordal short cycles”. Graphs Comb. Optim. vol. 60: 777-791. 2014. |
APA Style
Shunqin Liu. (2016). Smarandachely Adjacent-Vertex-Distinguishing Proper Edge Chromatic Number of Cm∨Kn. Applied and Computational Mathematics, 5(5), 202-206. https://doi.org/10.11648/j.acm.20160505.13
ACS Style
Shunqin Liu. Smarandachely Adjacent-Vertex-Distinguishing Proper Edge Chromatic Number of Cm∨Kn. Appl. Comput. Math. 2016, 5(5), 202-206. doi: 10.11648/j.acm.20160505.13
AMA Style
Shunqin Liu. Smarandachely Adjacent-Vertex-Distinguishing Proper Edge Chromatic Number of Cm∨Kn. Appl Comput Math. 2016;5(5):202-206. doi: 10.11648/j.acm.20160505.13
@article{10.11648/j.acm.20160505.13, author = {Shunqin Liu}, title = {Smarandachely Adjacent-Vertex-Distinguishing Proper Edge Chromatic Number of Cm∨Kn}, journal = {Applied and Computational Mathematics}, volume = {5}, number = {5}, pages = {202-206}, doi = {10.11648/j.acm.20160505.13}, url = {https://doi.org/10.11648/j.acm.20160505.13}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160505.13}, abstract = {According to different conditions, researchers have defined a great deal of coloring problems and the corresponding chromatic numbers. Such as, adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper total chromatic number. And we focus on the smarandachely adjacent-vertex-distinguishing proper edge chromatic number in this paper, study the smarandachely adjacent-vertex-distinguishing proper edge chromatic number of joint graph Cm∨Kn.}, year = {2016} }
TY - JOUR T1 - Smarandachely Adjacent-Vertex-Distinguishing Proper Edge Chromatic Number of Cm∨Kn AU - Shunqin Liu Y1 - 2016/10/17 PY - 2016 N1 - https://doi.org/10.11648/j.acm.20160505.13 DO - 10.11648/j.acm.20160505.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 202 EP - 206 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20160505.13 AB - According to different conditions, researchers have defined a great deal of coloring problems and the corresponding chromatic numbers. Such as, adjacent-vertex-distinguishing total chromatic number, adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper edge chromatic number, smarandachely-adjacent-vertex-distinguishing proper total chromatic number. And we focus on the smarandachely adjacent-vertex-distinguishing proper edge chromatic number in this paper, study the smarandachely adjacent-vertex-distinguishing proper edge chromatic number of joint graph Cm∨Kn. VL - 5 IS - 5 ER -