Global Dominator Coloring of Graphs

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Let SV. A vertex vV is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let 𝒞 = (V1, V2, . . ., Vk) be a coloring of G and let vV (G). A color class Vi is called a dom-color class or an anti domcolor class of the vertex v according as v is a dominator of Vi or an antidominator of Vi. The coloring 𝒞 is called a global dominator coloring of G if every vertex of G has a dom-color class and an anti dom-color class in 𝒞. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number and is denoted by χgd(G). This paper initiates a study on this notion of global dominator coloring.

[1] S. Arumugam, J. Bagga and K.R. Chandrasekar, On dominator colorings in graphs, Proc. Indian Acad. Sci. Math. Sci. 122 (2012) 561–571. doi:10.1007/s12044-012-0092-5

[2] S. Arumugam, T.W. Haynes, M.A. Henning and Y. Nigussie, Maximal independent sets in minimum colorings, Discrete Math. 311 (2011) 1158–1163. doi:10.1016/j.disc.2010.06.045

[3] G. Chartrand and Lesniak, Graphs and Digraphs, Fourth Edition (CRC Press, Boca Raton, 2005).

[4] R. Gera, On dominator coloring in graphs, Graph Theory Notes N.Y. 52 (2007) 25–30.

[5] R. Gera, S. Horton and C. Rasmussen, Dominator colorings and safe clique partitions, Congr. Numer. 181 (2006) 19–32.

[6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).

[7] J.E. Dunbar, S.M. Hedetniemi, S.T. Hedetniemi, D.P. Jacobs, D.J. Knisely, R. Laskar and D.F. Rall. Fall colorings of graphs, J. Combin. Math. Combin. Com-put. 33 (2000) 257–273.

[8] H.B. Merouane and M. Chellali, On the dominator colorings in trees, Discuss. Math. Graph Theory 32 (2012) 677–683. doi:10.7151/dmgt.1635

[9] L.B. Michaelraj, S.K. Ayyaswamy and S. Arumugam, Chromatic transversal domination in graphs, J. Combin. Math. Combin. Comput. 75 (2010) 33–40.

Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

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Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs


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