On total dominator coloring of middle graph, total graph and shadow graph
Downloads
Abstract
A total dominator coloring of a graph $G$ is a proper coloring of $G$ in which every vertex of the graph is adjacent to every vertex of some color class. The minimum number of colors required for a total dominator coloring of $G$ is called the total dominator chromatic number of $G$ and is denoted by $\chi_{t d}(G)$. In this paper we discuss some results on strict strong chromatic number of middle graph, total graph, and shadow graph.
Keywords:
Proper coloring, total dominator coloring, total dominator chromatic number, middle graph, total graph, shadow graphMathematics Subject Classification:
Mathematics- Pages: 731-734
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
S. Alikhani and N. Ghanbari, Total dominator chromatic number of specific graphs, arXiv: $1511.01652 mathrm{v} 1$.
G. Bagan, H.B. Merouane, M. Haddad and H. Kheddouci, On some domination colorings of graphs, Discrete Applied Mathematics, 230 (2017), 34-50.
J.A. Bondy and U.S.R. Murthy, Graph Theory with Applications, The Macmillan Press LTD, 1976.
R. Gera, S. Horton and C. Rasmussen, Dominator colorings and safe clique partitions, Congr. Numer, 181 (2006) 19.32.
N. Ghanbari and S. Alikhani, More on the total dominator chromatic number of a graph, Journal of Information and Optimization Sciences, DOI:10.1080/02522667.2018.1453665
S.M. Hedetniemi, S.T. Hedetniemi, A.A. Mcrae and J.R.S. Blair, Dominator coloring of graphs, (2006, preprint)
M.A. Henning, Total dominator colorings and total domination in graphs, Graphs and Combinatorics 31 (2015), 953-974.
A.P. Kazemi, Total dominator chromatic number of a graph, Transactions on Combinatorics, 4 (2014), 57-68.
A.P. Kazemi, Total dominator coloring in product graphs, Utilitas Mathematics, 94 (2014).
F. Kazemnejad and A.P. Kazemi, Total dominator coloring of central graphs, arXiv: 1801.05137.
A. Mohammed Abid and T.R. Ramesh Rao, Dominator Coloring of mycielskian graphs, Australasian Journal of Combinatorics 73 (2) (2019), 274-279.
A. Mohammed Abid and T.R. Ramesh Rao, Dominator Coloring changing and stable graphs upon vertex removal, Journal of Combin. Math and Combin. Comp. 112 (2020), 103-113.
A. Mohammed Abid and T.R. Ramesh Rao, On strict strong coloring of graphs, Discrete Mathematics, Algorithms and applications, https://doi.org/10.1142/S1793830921500403
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
