Back
 OJDM  Vol.6 No.2 , April 2016
On the Maximum Number of Dominating Classes in Graph Coloring
Abstract: 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].
Cite this paper: Zhou, B. (2016) On the Maximum Number of Dominating Classes in Graph Coloring. Open Journal of Discrete Mathematics, 6, 70-73. doi: 10.4236/ojdm.2016.62006.
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.

 
 
Top