scholarly journals Equitable total chromatic number of splitting graph

2019 ◽  
Vol 38 (4) ◽  
pp. 699-705
Author(s):  
G. Jayaraman ◽  
D. Muthuramakrishnan ◽  
K. Manikandan
Keyword(s):  
Chromatic Number ◽  
Total Chromatic Number ◽  
Splitting Graph

Splitting on classes of helm graphs and its equitabletotal chromatic number

2020 ◽  
pp. 635-642
Author(s):  
J. Veninstine Vivik ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Total Coloring ◽  
Total Chromatic Number ◽  
Splitting Graph

The equitable total coloring of a graph $G$ is the different colors used to color all the vertices and edges of $G$, in the order that adjacent vertices and edges are assigned with least different $k$-colors and can be partitioned into colors sets which differ by maximum one. The minimum of $k$-colors required is known as the equitable total chromatic number. In this paper the splitting graph of Helm and Closed Helm graph is constructed and its equitable total chromatic number is acquired.

scholarly journals Total chromatic number of one kind of join graphs

2006 ◽  
Vol 306 (16) ◽  
pp. 1895-1905 ◽  
Author(s):  
Guangrong Li ◽  
Limin Zhang
Keyword(s):  
Chromatic Number ◽  
Total Chromatic Number

A Characterization of Graphs with Fractional Total Chromatic Number Equal to

2009 ◽  
Vol 35 ◽  
pp. 235-240 ◽  
Author(s):  
Takehiro Ito ◽  
W. Sean Kennedy ◽  
Bruce A. Reed
Keyword(s):  
Chromatic Number ◽  
Total Chromatic Number

scholarly journals Total Coloring Conjecture for Certain Classes of Graphs

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 161 ◽  
Author(s):  
R. Vignesh ◽  
J. Geetha ◽  
K. Somasundaram
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Line Graph ◽  
Product Line ◽  
Total Coloring ◽  
Lexicographic Product ◽  
Total Chromatic Number ◽  
Minimum Number ◽  
Total Coloring Conjecture

A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color. The total chromatic number of a graph G, denoted by χ ′ ′ ( G ) , is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, Δ ( G ) + 1 ≤ χ ′ ′ ( G ) ≤ Δ ( G ) + 2 , where Δ ( G ) is the maximum degree of G. In this paper, we prove the total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph.

scholarly journals AVD-total-chromatic number of some families of graphs with Δ(G)=3

2017 ◽  
Vol 217 ◽  
pp. 628-638 ◽  
Author(s):  
Atílio G. Luiz ◽  
C.N. Campos ◽  
C.P. de Mello
Keyword(s):  
Chromatic Number ◽  
Total Chromatic Number

Total colorings of circulant graphs

2020 ◽  
pp. 2150050
Author(s):  
J. Geetha ◽  
K. Somasundaram ◽  
Hung-Lin Fu
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Total Coloring ◽  
Circulant Graphs ◽  
Total Chromatic Number ◽  
Number Formula ◽  
Total Coloring Conjecture

The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let [Formula: see text] denote the graphs of powers of cycles of order [Formula: see text] and length [Formula: see text] with [Formula: see text]. Then, [Formula: see text] In this paper, we prove the Campos and de Mello’s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles.

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 total chromatic number of Pseudo-Halin graphs with lower degree

2009 ◽  
Vol 309 (4) ◽  
pp. 982-986 ◽  
Author(s):  
Xianyong Meng ◽  
Jianhua Guo ◽  
Rensuo Li ◽  
Tao Chen ◽  
Bentang Su
Keyword(s):  
Chromatic Number ◽  
Lower Degree ◽  
Total Chromatic Number ◽  
Halin Graphs
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