Some characterization theorems on dominating chromatic partition-covering number of graphs
DOI:
https://doi.org/10.4067/S0716-09172014000100002Keywords:
Dominating set, chromatic partition, dominating chromatic partition-covering number, conjunto dominante, partición cromática, número de partición cromática dominante.Abstract
Let G = (V, E) be a graph of order n = |V| and chromatic number (G) A dominating set D of G is called a dominating chromatic partition-cover or dcc-set, if it intersects every color class of every X-coloring of G. The minimum cardinality of a dcc-set is called the dominating chromatic partition-covering number, denoted dcc(G). The dcc-saturation number equals the minimum integer i such that every vertex ν ∈ V is contained in a dcc-set of cardinality k.This number is denoted by dccs(G) In this paper we study a few properties ofthese two invariants dcc(G) and dccs(G).References
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[3] L. Benedict Michael Raj, S. K. Ayyaswamy, and S. Arumugam, Chromatic Transversal Domination in Graphs, J. Comb. Math. Comb. Computing, Vol. 75, pp. 33-40, (2010).
[4] G. Chartrand and P. Zang, Chromatic Graph Theory, CRC Press, Boca Raton, FL, (2009).
[5] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, (1969).
[6] F. Harary, S. Hedetneimi and R. Robinson, Uniquely Colorable Graphs, J. Combin. Theory 6, pp. 264-270, (1969).
[7] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker Inc., (1998).
[8] , Fundamentals of Domination in Graphs, Marcel Dekker Inc., (1998).
[9] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38, (Amer. Math Soc., Providence, RI), (1962).
Published
2017-03-23
How to Cite
[1]
L. B. Michael Raj and S. K. Ayyaswamy, “Some characterization theorems on dominating chromatic partition-covering number of graphs”, Proyecciones (Antofagasta, On line), vol. 33, no. 1, pp. 13-23, Mar. 2017.
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