The adjacent vertex distinguishing total coloring of planar graphs

2012 ◽  
Vol 27 (2) ◽  
pp. 379-396 ◽  
Author(s):  
Weifan Wang ◽  
Danjun Huang
Keyword(s):  
Planar Graphs ◽  
Total Coloring ◽  
Adjacent Vertex

Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 9

2019 ◽  
Vol 342 (5) ◽  
pp. 1392-1402
Author(s):  
Jie Hu ◽  
Guanghui Wang ◽  
Jianliang Wu ◽  
Donglei Yang ◽  
Xiaowei Yu
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Total Coloring ◽  
Adjacent Vertex

Adjacent vertex distinguishing total coloring of planar graphs with maximum degree 8

2020 ◽  
Vol 343 (10) ◽  
pp. 112014
Author(s):  
Yulin Chang ◽  
Jie Hu ◽  
Guanghui Wang ◽  
Xiaowei Yu
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Total Coloring ◽  
Adjacent Vertex

scholarly journals Adjacent vertex distinguishing indices of planar graphs without 3-cycles

2015 ◽  
Vol 338 (3) ◽  
pp. 139-148 ◽  
Author(s):  
Danjun Huang ◽  
Zhengke Miao ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Adjacent Vertex

Adjacent vertex distinguishing edge coloring of planar graphs without 3-cycles

2020 ◽  
Vol 12 (04) ◽  
pp. 2050035
Author(s):  
Danjun Huang ◽  
Xiaoxiu Zhang ◽  
Weifan Wang ◽  
Stephen Finbow
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Edge Coloring ◽  
Discrete Math ◽  
Adjacent Vertex ◽  
Chromatic Index ◽  
Proper Edge Coloring ◽  
Minimum Number

The adjacent vertex distinguishing edge coloring of a graph [Formula: see text] is a proper edge coloring of [Formula: see text] such that the color sets of any pair of adjacent vertices are distinct. The minimum number of colors required for an adjacent vertex distinguishing edge coloring of [Formula: see text] is denoted by [Formula: see text]. It is observed that [Formula: see text] when [Formula: see text] contains two adjacent vertices of degree [Formula: see text]. In this paper, we prove that if [Formula: see text] is a planar graph without 3-cycles, then [Formula: see text]. Furthermore, we characterize the adjacent vertex distinguishing chromatic index for planar graphs of [Formula: see text] and without 3-cycles. This improves a result from [D. Huang, Z. Miao and W. Wang, Adjacent vertex distinguishing indices of planar graphs without 3-cycles, Discrete Math. 338 (2015) 139–148] that established [Formula: see text] for planar graphs without 3-cycles.

List edge and list total coloring of 1-planar graphs

2012 ◽  
Vol 7 (5) ◽  
pp. 1005-1018 ◽  
Author(s):  
Xin Zhang ◽  
Jianliang Wu ◽  
Guizhen Liu
Keyword(s):  
Planar Graphs ◽  
Total Coloring ◽  
List Total Coloring

Adjacent vertex distinguishing edge colorings of planar graphs with girth at least five

2013 ◽  
Vol 28 (4) ◽  
pp. 893-909 ◽  
Author(s):  
Chengchao Yan ◽  
Danjun Huang ◽  
Dong Chen ◽  
Weifan Wang
Keyword(s):  
Planar Graphs ◽  
Adjacent Vertex ◽  
Edge Colorings
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