On global dominating -X-coloring of graphs

Rajeswari Malairaj, Sahul Hamid Isnail

Abstract


Let $G$ be a graph. Among all $\chi$-colorings of $G$, a coloring with the maximum number of color classes that are global dominating sets in $G$ is called a global dominating-$\chi$-coloring of $G$. The number of color classes that are global dominating sets in a global dominating-$\chi$-coloring of $G$ is defined to be the global dominating -$\chi$- color number of $G$, denoted by $gd_{\chi}(G)$. This concept was introduced in \cite{a78}. This paper extends the study of this notion.

Keywords


dominating -- coloring, global dominating -- coloring

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References


S. Arumugam, I. Sahul Hamid and A. Muthukamatchi, Independent domination and graph colorings, Ramanujan Mathematical Society Lecture Notes Series, 7(2008), 195--203.

S. Arumugam, Teresa W. Haynesb, Michael A. Henningc and Yared Nigussie, Maximal independent sets in minimum colorings, Discrete Mathematics, 311(2011), 1158--1163.

G. Chartrand and Lesniak, Graphs and Digraphs, Fourth edition, CRC press, Boca Raton, 2005.

J. John Arul Singh and R. Kala, Min-Dom-Color Number of a Graph, Int. J. Contemp. Math. Sciences, 5(2010), 2019--2027.

I. Sahul Hamid and M. Rajeswari, Global dominating sets in minimum coloring, Discrete Mathematics Algorithms and Applications,6(2014), No.3.




DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.2295

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