《山东大学学报(理学版)》 ›› 2018, Vol. 53 ›› Issue (12): 23-30.

• •

### 完全二部图K10,n(10≤n≤90)的点可区别E-全染色

1. 1.西北师范大学数学与统计学院, 甘肃 兰州 730070;2.宁夏大学数学统计学院, 宁厦 银川 750021
• 出版日期:2018-12-20 发布日期:2018-12-18
• 作者简介:包丽娅(1993— ),女,硕士研究生,研究方向为图论及其应用. E-mail:baoliya20170820bly@163.com
• 基金资助:
国家自然科学基金资助项目(11761064,61163037,11261046);宁夏自然科学基金资助项目(2018AAC03005);宁夏回族自治区百人计划资助项目

### Vertex-distinguishing E-total coloring of complete bipartite graph K10,n with 10≤n≤90

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
• Online:2018-12-20 Published:2018-12-18

Abstract: Let G be a simple graph. An E-total coloring f of G is called that if there are no two adjacent vertices of G receive the same color, and no edges of G receives the same color as one of its endpoints. For an E-total coloring f of G, if C(u)≠C(v) for any two distinct vertices u and v of V(G), where C(x) denotes the set of colors of vertex x and of the edges incident with x under f, then f is called a vertex-distinguishing E-total coloring of G. Let χevt(G)=min{k|G has a k-VDET coloring}. Then χevt(G) is called the VDET chromatic number of G. By using analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K10,n is discussed and the VDET chromatic number of K10,n(10≤n≤90) has been obtained.

• O157.5
 [1] ZHANG Zhongfu, QIU Pengxiang, LI Jingwen, et al. Vertex-distinguishing total colorings of graphs[J]. Ars Combinatoria, 2008, 87:33-45.[2] CHEN Xiangen, GAO Yuping, YAO Bing. Relations of vertex distinguishing total chromatic numbers between a subgraph and its supergraph[J]. Information Sciences, 2014, 288:246-253.[3] 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(理学版), 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.[4] 陈祥恩, 王治文, 马彦荣, 等. mK4的点可区别全染色[J]. 吉林大学学报(理学版), 2012, 50(4):686-692. CHEN Xiangen, WANG Zhiwen, MA Yanrong, et al. Vertex-distinguishing total colorings of mK4[J]. Journal of Jilin University(Science Edition), 2012, 50(4):686-692.[5] CHEN Xiangen, ZU Yue, ZHANG Zhongfu. Vertex-distinguishing E-total colorings of graphs[J]. Arab J Sci Eng, 2011, 36:1485-1500.[6] CHEN Xiangen, ZU Yue. Vertex-distinguishing E-total coloring of the graphs mC3 and mC4[J]. Journal of Mathematical Research & Exposition, 2011, 31:45-58.[7] 李世玲, 陈祥恩, 王治文. 完全二部图K3,n(3≤n≤17)的点可区别E-全染色[J]. 吉林大学学报(理学版), 2015, 53(6):1171-1176. LI Shiling, CHEN Xiangen,WANG Zhiwen. Vertex-distinguishing E-total coloring of complete bipartite graph K3,n when 3≤n≤17[J]. Journal of Jilin University(Science Edition), 2015, 53(6):1171-176.[8] 李世玲, 陈祥恩, 王治文. 完全二部图K3,n(n≥18)的点可区别E-全染色[J]. 山东大学学报(理学版), 2015, 51(4):68-71. LI Shiling, CHEN Xiangen, WANG Zhiwen. Vertex-distinguishing E-total coloring of complete bipartite graph K3,n when n≥18[J]. Journal of Shandong University(Nature Science), 2015, 51(4):68-71.[9] 李世玲. 完全二部图的点可区别E-全染色的若干结果[D]. 兰州:西北师范大学, 2017. LI Shiling. Some results of Vertex-distinguishing E-total coloring of complete bipartite graph[D]. Lanzhou: Northwest Normal University, 2017.[10] CHEN Xiangen. Vertex-distinguishing E-total coloring of complete bipartite graph K7,n when 7≤n≤95[J]. Communications in Mathematical Research, 2016, 32(4):359-374.
 [1] 寇艳芳,陈祥恩,王治文. K1,3,p和 K1,4,p的点可区别的IE-全染色及一般全染色[J]. 山东大学学报（理学版）, 2018, 53(8): 53-60. [2] 李世玲, 陈祥恩,王治文. 完全二部图K3,n(n≥18)的点可区别E-全染色[J]. 山东大学学报（理学版）, 2016, 51(4): 68-71. [3] 刘信生, 邓卫东, 王志强. 直积图邻点可区别E-全染色的一些结论[J]. 山东大学学报（理学版）, 2015, 50(02): 5-8. [4] 李振琳,卢君龙,吕新忠. 关于图的符号边全控制[J]. J4, 2012, 47(6): 83-86. [5] 王国兴. 点不交的m个C3的并的点可区别IE-全染色[J]. J4, 2011, 46(2): 57-61. [6] 何文玉， 陈祥恩*. 完全二部图K5,n的点可区别IE全染色[J]. J4, 2009, 44(2): 91-96.
Viewed
Full text

Abstract

Cited

Shared
Discussed
 [1] 杨军. 金属基纳米材料表征和纳米结构调控[J]. 山东大学学报（理学版）, 2013, 48(1): 1 -22 . [2] 孙小婷1,靳岚2*. DOSY在寡糖混合物分析中的应用[J]. J4, 2013, 48(1): 43 -45 . [3] 杨伦，徐正刚，王慧*，陈其美，陈伟，胡艳霞，石元，祝洪磊，曾勇庆*. RNA干扰沉默PID1基因在C2C12细胞中表达的研究[J]. J4, 2013, 48(1): 36 -42 . [4] 杨莹,江龙*,索新丽. 容度空间上保费泛函的Choquet积分表示及相关性质[J]. J4, 2013, 48(1): 78 -82 . [5] 李永明1, 丁立旺2. PA误差下半参数回归模型估计的r-阶矩相合[J]. J4, 2013, 48(1): 83 -88 . [6] 杨永伟1,2,贺鹏飞2,李毅君2,3. BL-代数的严格滤子[J]. 山东大学学报（理学版）, 2014, 49(03): 63 -67 . [7] 赵同欣1,刘林德1*,张莉1,潘成臣2,贾兴军1. 紫藤传粉昆虫与花粉多型性研究[J]. 山东大学学报（理学版）, 2014, 49(03): 1 -5 . [8] 汤晓宏1，胡文效2*，魏彦锋2，蒋锡龙2，张晶莹2，. 葡萄酒野生酿酒酵母的筛选及其生物特性的研究[J]. 山东大学学报（理学版）, 2014, 49(03): 12 -17 . [9] 王碧玉,曹小红*. 算子矩阵的Browder定理的摄动[J]. 山东大学学报（理学版）, 2014, 49(03): 90 -95 . [10] 于秀清. P-集合的(σ,τ)-扩展模型与其性质[J]. 山东大学学报（理学版）, 2014, 49(04): 90 -94 .