On the Maximum Number of Dominating Classes in Graph Coloring

Subject Areas : Statistics

M. Faghani ¹ ( Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran )

Received: 2017-09-25 Accepted : 2018-09-05 Published : 2019-12-22

Keywords: عدد رنگی احاطه گر, رنگ آمیزی گراف, عدد رنگی, رده های رنگ آمیزی احاطه گر, مجموعه های احاطه گر,

Abstract :

In this paper we investigate the dominating- -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 H. 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., Maximal Independent Sets in Minimum Colorings. Discrete Mathematics, 311 (2011) 1158-1163.

 

[2] Arumugam, A., Hamid, I.S. and Muthukamatchi, A., Independent Domination and Graph Clorings. Ramanujan Mathematical Society Lecture Notes Series, 7 (2008) 195-203. 

 

[3] Arumugam, S. and Chandrasekar, K.R., Minimal Dominating Sets in Maximum Domatic Partitions. Australasian Journal of Combinatorics, 52 (2012) 281-292. 

 

[4] Li, S., Zhang, H. and Zhang, X., Maximal Independent Sets in Bipartite Graphs with at Least One Cycle. Discrete Mathematics and Theoretical Computer Science, 15 (2013) 243-258.