An improved upper bound on the adjacent vertex distinguishing total chromatic number of graphs

2018 ◽  
Vol 341 (5) ◽  
pp. 1472-1478 ◽  
Author(s):  
Bojan Vučković
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
Adjacent Vertex ◽  
Total Chromatic Number

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.

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 General Vertex-Distinguishing Total Coloring of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chanjuan Liu ◽  
Enqiang Zhu
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
Total Coloring ◽  
Total Chromatic Number ◽  
Minimum Integer

The general vertex-distinguishing total chromatic number of a graphGis the minimum integerk, for which the vertices and edges ofGare colored usingkcolors such that any two vertices have distinct sets of colors of them and their incident edges. In this paper, we figure out the exact value of this chromatic number of some special graphs and propose a conjecture on the upper bound of this 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

A Note on the Adjacent Vertex Distinguishing Total Chromatic Number of Graph

2011 ◽  
Vol 474-476 ◽  
pp. 2341-2345
Author(s):  
Zhi Wen Wang
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Simple Graph ◽  
Total Coloring ◽  
Adjacent Vertex ◽  
Total Chromatic Number ◽  
Parallel Graph ◽  
Total Coloring Conjecture

A total coloring of a simple graph G is called adjacent vertex distinguishing if for any two adjacent and distinct vertices u and v in G, the set of colors assigned to the vertices and the edges incident to u differs from the set of colors assigned to the vertices and the edges incident to v. In this paper we shall prove the series-parallel graph with maximum degree 3 and the series-parallel graph whose the number of edges is the double of maximum degree minus 1 satisfy the adjacent vertex distinguishing total coloring conjecture.

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