On the D(2)-Vertex Distinguishing Total Coloring of Graphs with Δ=3

被引：0

作者：

Wen, Fei ^{[1
]}

Jia, Xiuqing ^{[1
]}

Li, Zepeng ^{[2
]}

Li, Muchun ^{[1
]}

机构：

[1] Lanzhou Jiaotong Univ, Inst Appl Math, Lanzhou 730070, Peoples R China

[2] Lanzhou Univ, Sch Informat Sci & Engn, Lanzhou 730000, Peoples R China

来源：

MATHEMATICAL NOTES | 2022年 / 112卷 / 1-2期

关键词：

total coloring; D(2)-vertex-distinguishing total coloring; D(2)-vertex-distinguishing total chromatic number; TOTAL CHROMATIC NUMBER;

D O I：

10.1134/S000143462207015X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A D(2)-vertex-distinguishing total coloring of a graph G is a proper total coloring such that no pair of vertices, within distance two, has the same set of colors, and the minimum number of colors required for such a coloring is called D(2)-vertex-distinguishing total chromatic number of G, and denoted by chi(2vt)(G). In this paper, we prove that chi(2vt)(G)<= 11 for any graph G with Delta(G)=3.

引用

页码：142 / 149

页数：8

共 15 条

[1] Adjacent vertex distinguishing edge-colorings
Balister, P. N.
Gyori, E.
Lehel, J.
Schelp, R. H.
[J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2007, 21 (01) : 237 - 250
[2] Bondy JA., 1976, GRAPH THEORY APPL, DOI [10.1007/978-1-349-03521-2, DOI 10.1007/978-1-349-03521-2]
[3] Chen X.E., 2015, INTRO DISTINGUISHING
[4] On the adjacent vertex distinguishing total coloring numbers of graphs with Δ=3
Chen, Xiang'en
[J]. DISCRETE MATHEMATICS, 2008, 308 (17) : 4003 - 4007
[5] Cheng XH, 2017, J COMB OPTIM, V34, P383, DOI 10.1007/s10878-016-9995-x
[6] List-coloring the square of a subcubic graph
Cranston, Daniel W.
Kim, Seog-Jin
[J]. JOURNAL OF GRAPH THEORY, 2008, 57 (01) : 65 - 87
[7] Neighbor Sum Distinguishing Total Colorings of Corona of Subcubic Graphs
Dong, Aijun
Zhang, Wenwen
Tan, Xiang
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (04) : 1919 - 1926
[8] A note on the adjacent vertex distinguishing total chromatic number of graphs
Huang, Danjun
Wang, Weifan
Yan, Chengchao
[J]. DISCRETE MATHEMATICS, 2012, 312 (24) : 3544 - 3546
[9] NEIGHBOR SUM DISTINGUISHING TOTAL CHOOSABILITY OF IC-PLANAR GRAPHS
Song, Wen-Yao
Miao, Lian-Ying
Duan, Yuan-Yuan
[J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2020, 40 (01) : 331 - 344
[10] Neighbor sum distinguishing total choosability of 1-planar graphs with maximum degree at least 24
Sun, Lin
Yu, Guanglong
Li, Xin
[J]. DISCRETE MATHEMATICS, 2021, 344 (01)

← 1 2 →