We investigate
the dominating-c-color number,, of a
graph G. That is the maximum number
of color classes that are also dominating when G is colored using colors. We show that where is the join of G and . This
result allows us to construct classes of graphs such that and thus provide some information regarding two
questions raised in [1] and [2].
References
[1]
Arumugam, S., Haynes, T.W., Henning, M.A. and Nigussie, Y. (2011) Maximal Independent Sets in Minimum Colorings. Discrete Mathematics, 311, 1158-1163. http://dx.doi.org/10.1016/j.disc.2010.06.045
[2]
Arumugam, A., Hamid, I.S. and Muthukamatchi, A. (2008) Independent Domination and Graph Clorings. Ramanujan Mathematical Society Lecture Notes Series, 7, 195-203.
[3]
Arumugam, S. and Chandrasekar, K.R. (2012) Minimal Dominating Sets in Maximum Domatic Partitions. Australasian Journal of Combinatorics, 52, 281-292.
[4]
Li, S., Zhang, H. and Zhang, X. (2013) Maximal Independent Sets in Bipartite Graphs with at Least One Cycle. Discrete Mathematics and Theoretical Computer Science, 15, 243-258.
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