Total coloring of middle graph, total graph of twig graph and comb graph

2020 ◽  
Vol 14 (5) ◽  
Keyword(s):  
Total Coloring ◽  
Total Graph ◽  
Middle Graph

A modified anti-magic graph labeling for middle graph and total graph related to path

2016 ◽  
Author(s):  
Zareen Tasneem ◽  
Farissa Tafannum ◽  
Maksuda Rahman Anti ◽  
Wali Mohammad Abdullah ◽  
Md. Mahbubur Rahman
Keyword(s):  
Graph Labeling ◽  
Total Graph ◽  
Middle Graph

scholarly journals ON DYNAMIC COLORING OF WEB GRAPH

2018 ◽  
Vol 5 (2) ◽  
pp. 11-15
Author(s):  
Aaresh R.R ◽  
Venkatachalam M ◽  
Deepa T
Keyword(s):  
Chromatic Number ◽  
Line Graph ◽  
Proper Coloring ◽  
Total Graph ◽  
Web Graph ◽  
Middle Graph

Dynamic coloring of a graph G is a proper coloring. The chromatic number of a graph G is the minimum k such that G has a dynamic coloring with k colors. In this paper we investigate the dynamic chromatic number for the Central graph, Middle graph, Total graph and Line graph of Web graph Wn denoted by C(Wn), M(Wn), T(Wn) and L(Wn) respectively.

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.

scholarly journals Some New Results on Distance k-Domination in Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Samir K. Vaidya ◽  
Nirang J. Kothari
Keyword(s):  
Domination Number ◽  
Total Graph ◽  
Middle Graph ◽  
Domination In Graphs

We determine the distance k-domination number for the total graph, shadow graph, and middle graph of path Pn.

scholarly journals A note on achromatic coloring of star graph families

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 251-255 ◽  
Author(s):  
Vivin Vernold ◽  
M. Venkatachalam ◽  
Ali Akbar
Keyword(s):  
Star Graph ◽  
Total Graph ◽  
Middle Graph ◽  
Graph Families

In this paper, we find the achromatic number of central graph, middle graph and total graph of star graph, denoted by C(K1,n), M(K1,n) and T(K1,n) respectively.

Coloring 3-power of 3-subdivision of subcubic graph

2018 ◽  
Vol 10 (03) ◽  
pp. 1850041 ◽  
Author(s):  
Fang Wang ◽  
Xiaoping Liu
Keyword(s):  
Positive Integer ◽  
Chromatic Number ◽  
London Math ◽  
Total Coloring ◽  
Total Graph ◽  
Total Chromatic Number ◽  
Subcubic Graph ◽  
Minimum Integer ◽  
Vertex Set ◽  
Number Formula

Let [Formula: see text] be a graph and [Formula: see text] be a positive integer. The [Formula: see text]-subdivision [Formula: see text] of [Formula: see text] is the graph obtained from [Formula: see text] by replacing each edge by a path of length [Formula: see text]. The [Formula: see text]-power [Formula: see text] of [Formula: see text] is the graph with vertex set [Formula: see text] in which two vertices [Formula: see text] and [Formula: see text] are adjacent if and only if the distance [Formula: see text] between [Formula: see text] and [Formula: see text] in [Formula: see text] is at most [Formula: see text]. Note that [Formula: see text] is the total graph [Formula: see text] of [Formula: see text]. The chromatic number [Formula: see text] of [Formula: see text] is the minimum integer [Formula: see text] for which [Formula: see text] has a proper [Formula: see text]-coloring. The total chromatic number of [Formula: see text], denoted by [Formula: see text], is the chromatic number of [Formula: see text]. Rosenfeld [On the total coloring of certain graphs, Israel J. Math. 9 (1971) 396–402] and independently, Vijayaditya [On total chromatic number of a graph, J. London Math. Soc. 2 (1971) 405–408] showed that for a subcubic graph [Formula: see text], [Formula: see text]. In this note, we prove that for a subcubic graph [Formula: see text], [Formula: see text].

scholarly journals On total dominator coloring of middle graph, total graph and shadow graph

2021 ◽  
Vol 9 (1) ◽  
pp. 731-734
Author(s):  
S. Baskaran ◽  
A.M. Shahul Hameed
Keyword(s):  
Total Graph ◽  
Middle Graph ◽  
Dominator Coloring

scholarly journals Some New Results on Super Heronian Mean

2017 ◽  
Vol 9 (1) ◽  
pp. 62
Author(s):  
Labelling S. S. Sandhya ◽  
E. Ebin Raja Merly ◽  
G. D. Jemi
Keyword(s):  
The Other ◽  
Total Graph ◽  
Middle Graph ◽  
Heronian Mean ◽  
Valid Information

Here we discuss on Some new results on Super Heronian Mean Labelling of graphs. For the present investigation on Qn ⨀ K1,D(Qn) ⨀ K1,Middle graph, Total graph, Ln ⨀ K1.We discuss briefly about the summary and the other valid information with appropriate graphs and definitions. 

On b-chromatic number of theta graph families

2020 ◽  
pp. 643-650
Author(s):  
M. Vinitha ◽  
M. Venkatachalam
Keyword(s):  
Chromatic Number ◽  
Line Graph ◽  
Total Graph ◽  
Middle Graph ◽  
Graph Families

In this paper, we investigate the $b$-chromatic number for the theta graph $\theta(s_1, s_2, \cdots, s_n)$, middle graph of theta graph $M(G)$, total graph of theta graph $T(G)$, line graph of theta graph $L(G)$ and the central graph of theta graph $C(G)$.

scholarly journals On the r-dynamic coloring of some fan graph families

2021 ◽  
Vol 29 (3) ◽  
pp. 151-181
Author(s):  
Raúl M. Falcón ◽  
M. Venkatachalam ◽  
S. Gowri ◽  
G. Nandini
Keyword(s):  
Chromatic Number ◽  
Line Graph ◽  
Graph Invariant ◽  
Total Graph ◽  
Sharp Bounds ◽  
Middle Graph ◽  
Graph Families ◽  
Fan Graph

Abstract In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph M(Fm,n ), the total graph T (Fm,n ), the central graph C(Fm,n ) and the line graph L(Fm,n ). In addition, we determine the r-dynamic chromatic number of each one of these four families of graphs in case of being m = 1.

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