On the Equitable Edge-Coloring of 1-Planar Graphs and Planar Graphs

2017 ◽  
Vol 33 (4) ◽  
pp. 945-953 ◽  
Author(s):  
Dai-Qiang Hu ◽  
Jian-Liang Wu ◽  
Donglei Yang ◽  
Xin Zhang
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Equitable Edge Coloring

A STUDY ON FUZZY EQUITABLE EDGE COLORING OF WHEEL RELATED GRAPHS

2020 ◽  
Vol 9 (11) ◽  
pp. 9311-9317
Author(s):  
K. Sivaraman ◽  
R.V. Prasad
Keyword(s):  
Edge Coloring ◽  
Graph Labeling ◽  
Equitable Edge Coloring

Equitable edge coloring is a kind of graph labeling with the following restrictions. No two adjacent edges receive same label (color). and number of edges in any two color classes differ by at most one. In this work we are going to present the Fuzzy equitable edge coloring of some wheel related graphs.

scholarly journals Acyclic edge coloring conjecture is true on planar graphs without intersecting triangles

2021 ◽  
Author(s):  
Qiaojun Shu ◽  
Yong Chen ◽  
Shuguang Han ◽  
Guohui Lin ◽  
Eiji Miyano ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Acyclic Edge Coloring

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.

Acyclic Edge Coloring of IC-planar Graphs

2020 ◽  
Vol 36 (3) ◽  
pp. 581-589
Author(s):  
Wen-yao Song ◽  
Yuan-yuan Duan ◽  
Juan Wang ◽  
Lian-ying Miao
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Acyclic Edge Coloring

A self-stabilizing ()-edge-coloring algorithm for planar graphs in anonymous uniform systems

2007 ◽  
Vol 101 (4) ◽  
pp. 168-173 ◽  
Author(s):  
Chi-Hung Tzeng ◽  
Jehn-Ruey Jiang ◽  
Shing-Tsaan Huang
Keyword(s):  
Planar Graphs ◽  
Edge Coloring

scholarly journals Acyclic edge coloring of planar graphs with large girth

2009 ◽  
Vol 410 (47-49) ◽  
pp. 5196-5200 ◽  
Author(s):  
Dongxiao Yu ◽  
Jianfeng Hou ◽  
Guizhen Liu ◽  
Bin Liu ◽  
Lan Xu
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
Acyclic Edge Coloring ◽  
Large Girth
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