An upper bound for the total chromatic number

1990 ◽  
Vol 6 (2) ◽  
pp. 153-159 ◽  
Author(s):  
H. R. Hind
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
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.

An Improvement of Hind's Upper Bound on the Total Chromatic Number

1996 ◽  
Vol 5 (2) ◽  
pp. 99-104 ◽  
Author(s):  
Amanda Chetwynd ◽  
Roland Häggkvist
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
Chromatic Index ◽  
Total Chromatic Number

We show that the total chromatic number of a simple k-chromatic graph exceeds the chromatic index by at most 18k ⅓ log ½ 3k.

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 On r-dynamic coloring of comb graphs

2021 ◽  
Vol 27 (2) ◽  
pp. 191-200
Author(s):  
K. Kalaiselvi ◽  
◽  
N. Mohanapriya ◽  
J. Vernold Vivin ◽  
◽  
...  
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Upper Bound ◽  
Line Graph ◽  
Proper Coloring ◽  
Total Graph ◽  
Middle Graph ◽  
Different Color

An r-dynamic coloring of a graph G is a proper coloring of G such that every vertex in V(G) has neighbors in at least $\min\{d(v),r\}$ different color classes. The r-dynamic chromatic number of graph G denoted as $\chi_r (G)$, is the least k such that G has a coloring. In this paper we obtain the r-dynamic chromatic number of the central graph, middle graph, total graph, line graph, para-line graph and sub-division graph of the comb graph $P_n\odot K_1$ denoted by $C(P_n\odot K_1), M(P_n\odot K_1), T(P_n\odot K_1), L(P_n\odot K_1), P(P_n\odot K_1)$ and $S(P_n\odot K_1)$ respectively by finding the upper bound and lower bound for the r-dynamic chromatic number of the Comb graph.

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