On Adjacent Vertex-Distinguishing Total Chromatic Number of Generalized Petersen Graphs

2016 ◽  
Author(s):  
Enqiang Zhu ◽  
Fei Jiang ◽  
Zepeng Li ◽  
Zehui Shao ◽  
Jin Xu
Keyword(s):  
Chromatic Number ◽  
Adjacent Vertex ◽  
Total Chromatic Number ◽  
Generalized Petersen Graphs ◽  
Petersen Graphs

The Smarandachely Adjacent Vertex Distinguishing E-Total Coloring of some Join Graphs

2013 ◽  
Vol 475-476 ◽  
pp. 379-382
Author(s):  
Mu Chun Li ◽  
Shuang Li Wang ◽  
Li Li Wang
Keyword(s):  
Chromatic Number ◽  
Total Coloring ◽  
Adjacent Vertex ◽  
Analysis Method ◽  
Total Chromatic Number ◽  
Join Graph ◽  
Total Coloring Conjecture

Using the analysis method and the function of constructing the Smarandachely adjacent vertex distinguishing E-total coloring function, the Smarandachely adjacent vertex distinguishing E-total coloring of join graphs are mainly discussed, and the Smarandachely adjacent vertex distinguishing E-total chromatic number of join graph are obtained. The Smarandachely adjacent vertex distinguishing E-total coloring conjecture is further validated.

CERTAIN OPERATION OF GENERALIZED PETERSEN GRAPHS HAVING LOCATING-CHROMATIC NUMBER FIVE

2020 ◽  
Vol 24 (2) ◽  
pp. 83-97
Author(s):  
Agus Irawan ◽  
Asmiati ◽  
S. Suharsono ◽  
Kurnia Muludi ◽  
La Zakaria
Keyword(s):  
Chromatic Number ◽  
Generalized Petersen Graphs ◽  
Petersen Graphs

scholarly journals Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Ramy Shaheen ◽  
Ziad Kanaya ◽  
Khaled Alshehada
Keyword(s):  
Chromatic Number ◽  
Proper Coloring ◽  
Game Chromatic Number ◽  
Generalized Petersen Graphs ◽  
Minimum Number ◽  
Petersen Graphs ◽  
Jahangir Graph ◽  
Prism Graph

Let G = V , E be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph G a proper coloring where no two adjacent vertices are signed with the same color. Alice's goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by χ g G , while Bob's goal is to prevent Alice's goal. In this paper, we investigate the game chromatic number χ g G of Generalized Petersen Graphs G P n , k for k ≥ 3 and arbitrary n , n -Crossed Prism Graph, and Jahangir Graph J n , m .

scholarly journals The adjacent vertex distinguishing total chromatic number

2012 ◽  
Vol 312 (17) ◽  
pp. 2741-2750 ◽  
Author(s):  
Tom Coker ◽  
Karen Johannson
Keyword(s):  
Chromatic Number ◽  
Adjacent Vertex ◽  
Total Chromatic Number

scholarly journals On Adjacent Vertex-distinguishing Equitable-total Chromatic Number of Pm ∨ Fm

2021 ◽  
Vol 1744 (4) ◽  
pp. 042204
Author(s):  
Jishun Wang ◽  
Minlun Yan ◽  
Renfu Ge ◽  
Bujun Li
Keyword(s):  
Chromatic Number ◽  
Adjacent Vertex ◽  
Total Chromatic Number
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