JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 24-30.doi: 10.6040/j.issn.1671-9352.0.2016.615

Previous Articles     Next Articles

Vertex-distinguishing total coloring of mC8

HE Yu-ping1, WANG Zhi-wen2, CHEN Xiang-en1*   

  1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. College of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China
  • Received:2016-12-29 Online:2017-10-20 Published:2017-10-12

PDF (PC)

359

Abstract: The vertex-distinguishing total colorings of disjoint union of mC8 are discussed and the vertex-distinguishing total chromatic numbers of these graphs is determined. The result in this paper illustrated the VDTC conjecture is valid for these graphs.

Key words: cycle, vertex-distinguishing total coloring, vertex-distinguishing total chromatic number, proper total coloring

CLC Number: 

  • O157.5
[1] BURRIS A C, SCHELP R H. Vertex-distinguishing proper edge-colorings[J]. Journal of Graph Theory, 2015, 26(2):73-82.
[2] BALISTER P N, RIORDAN O M, SCHELP R H. Vertex-distinguishing edge colorings of graphs[J]. Journal of Graph Theory, 2003, 42:95-109.
[3] BAZGAN C, HARKAT-BENHAMDINE A, LI H, et al. On the vertex-distinguishing proper edge-colorings of graphs[J]. Journal of Combinatorial Theory, 1999, 75(2):288-301.
[4] ZHANG Zhongfu, QIU Pengxiang, XU Baogen, et al. Vertex-distinguishing total colorings of graphs[J]. Ars Combinatoria, 2008, 87:33-45.
[5] 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. CHEN Xiangen. An introduction to the distinguish coloring of graphs[M]. Beijing: Science and Technology of China Press, 2015.
[6] 辛小青, 王治文, 陈祥恩,等. 点不交的m个C3的并的点可区别全染色[J]. 吉林大学学报(自然科学版), 2012,50(2):251-257. XIN Xiaoqing, WANG Zhiwen, CHEN Xiangen, et al. Vertex-distinguishing total chromatic number of mC3[J]. Journal of Jilin University(Science Edition), 2012, 50(2):251-257.
[7] 辛小青, 陈祥恩. m个点不交的C4的并的点可区别全染色[J]. 山东大学学报(理学版), 2010,45(10):35-39. XIN Xiaoqing, CHEN Xiangen. Vertex-distinguishing total chromatic number of mC4[J]. Journal of Shandong University(Natural Science), 2010, 45(10):35-39.
[8] CHEN Xiangen, MA Yanrong, YANG Fang, et al.Vertex-distinguishing total colorings of mC5[J]. Applied Mechanics and Materials, 2013, 321-324:578-581.
[1] FANG Qi-ming, ZHANG Li. k-frugal list coloring of planar graphs without 4 and 5-cycles [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 35-41.
[2] WANG Xiao-li, WANG Hui-juan, LIU Bin. Total coloring of planar graphs with maximum degree seven [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 100-106.
[3] CHEN Hong-yu, ZHANG Li. Linear 2-arboricity of planar graphs with 4-cycles have no common vertex [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 36-41.
[4] YU Xiao-lan. Global dimensions of cocycle deformations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 39-43.
[5] TAN Xiang. Total colorings of planar graphs without 6-cycles and adjacent 5-cycles [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 72-78.
[6] BAI Dan, ZUO Lian-cui. The(d,1)-total labelling of the cube of cycles [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 59-64.
[7] WANG Jia-jiang, CHEN Ling, MEN Yu-tao, JI Chen. The feasibility study on shorten treatment cycle of dental implantation and split-root technique joint repair [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(3): 40-43.
[8] WU Zi-juan, CHEN Yuan-yuan, ZHANG Liang-yun. Quasidimodule algebras over Hopf quasigroups and Yetter-Drinfeld quasimodule algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 28-33.
[9] XUE Li-xia, LI Zhi-hui, XIE Jia-li. A note on the optimal information rate of hypercycle access structure with three hyperedges [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(11): 60-66.
[10] WANG Shan-shan, QI En-feng. On the number of contractible edges of longest cycles in k-connected graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 27-31.
[11] MENG Xian-qing. Strong edge coloring of a class of planar graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 10-13.
[12] HE Xue, TIAN Shuang-liang. Adjacent vertex-distinguishing edge/total colorings of double graph of some graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 63-66.
[13] LI Jing-wen, JIA Xi-bei, DONG Wei, LI Xiao-hui, YAN Guang-hui. The algorithm for adjacent-vertex-distinguishing total coloring of graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 14-21.
[14] ZHANG Shao-hua, YAN Jin, LI Shuo. Disjoint 4-cycles and 8-cycles in graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 1-4.
[15] CHEN Hong-yu1, ZHANG Li2. The linear 2-arboricity of planar graphs without 5-, 6-cycles with chord [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 26-30.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd