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Characterization Of Strong And Weak Dominating - Color Number In A Graph
[Full Text]
AUTHOR(S)
T.Ramachandran, D.Udayakumar, A.Naseer Ahmed
KEYWORDS
Index Terms: Dominating--color number, Strong dominating -color number, Weak dominating -color number.
ABSTRACT
Abstract: Strong dominating - color number of a graph G is defined as the maximum number of color classes which are strong dominating sets of G, and is denoted by sd_ (G). Similarly, weak dominating - color number of a graph G is defined as the maximum number of color classes which are weak dominating sets of G, and is denoted by wd_ (G). In both the cases, the maximum is taken over all -coloring of G. In this paper, some bounds for sd_ (G) and wd_ (G) are obtained and characterized the graphs for which strong dominating - color number and strong dominating - color number exist. Finally, Nordhaus-Gaddum inequalities for sd_ (G) and wd_ (G) is derived.
REFERENCES
Douglas B. West, Introduction to Graph Theory, 2nd Edition (Prentice Hall, Inc, Mass, 2001).
Dieter Rautenbach, Bounds on the strong domination number, Discrete Mathematics, 215, 2000, 201-212.
E. Sampathkumar and L. PushpaLatha, Strong, Weak Domination and Domination Balance in a Graph, Discrete Math., 161, 1996, 235-242.
Harary, E., Graph Theory (Addison Wesley, Reading, Mass, 1972).
S. Arumugam, I. Sahul Hamid and A. Muthukamatchi, Independent Domination and Graph Colorings, In: Proceedings of International Conference on Discrete Mathematics. Lecture Note series in Mathematics, Ramanujan Mathematical Society, India, 2008, 224-232.
T.Ramachandran, A.Naseer Ahmed, Strong and Weak Dominating - Color Number of K -Partite Graph, International Journal of Advanced Technology in Engineering and Science, ISSN (online): 2348 – 7550.
T.Ramachandran and A.Naseer Ahmed, Strong dominating - color number of some graph, Math. Sci. Int. Res. Journal, Vol 2, Iss 2, 2013.
S. Arumugam, Teresa W.Haynes, Michael A. Henning, YaredNigussie, Maximal independent sets in minimum colorings, Discrete Mathematics, 311, pp1158-1163, 2011
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