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

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

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.

scholarly journals A note on the adjacent vertex distinguishing total chromatic number of graphs

2012 ◽  
Vol 312 (24) ◽  
pp. 3544-3546 ◽  
Author(s):  
Danjun Huang ◽  
Weifan Wang ◽  
Chengchao Yan
Keyword(s):  
Chromatic Number ◽  
Adjacent Vertex ◽  
Total Chromatic Number

Adjacent Vertex-Distinguishing E-Total Coloring on the Multiple Join Graph of Several Kinds of Particular Graphs

2012 ◽  
Vol 546-547 ◽  
pp. 489-494
Author(s):  
Mu Chun Li ◽  
Li Zhang
Keyword(s):  
Positive Integer ◽  
Chromatic Number ◽  
Simple Graph ◽  
Total Coloring ◽  
Adjacent Vertex ◽  
Total Chromatic Number ◽  
Join Graph ◽  
Uv C

Let G(V,E) be a simple graph, k be a positive integer, f be a mapping from V(G)E(G) to 1,2,...k. If uvE(G), we have f(u)≠f(v),f(u)≠f(uv) ,f(v)≠f(uv) ,C(u)≠C(v) , where C(u). Then f is called the adjacent vertex-distinguishing E-total coloring of G. The number is called the adjacent vertex –distinguishing E-total chromatic number of G. In this paper, the adjacent vertex –distinguishing E-total chromatic number of the multiple join graph of several kinds of particular graphs is discussed by using construct coloring function.

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