GLOBAL COLOR CLASS DOMINATION PARTITION OF A GRAPH

Abstract

Color class domination partition was suggested by E. Sampathkumar and it was studied in [1]. A proper color partition of a nite, simple graph G is called a color class domination partition or cd-partition if every color class is dominated by a vertex. This concept is dierent from dominator color partition introduced in [[2], [3]] where every vertex dominates a color class. Suppose G has no full degree vertex that is, a vertex which is adjacent with every other vertex of the graph . Then a color class may be independent from a vertex outside the class. This leads to Global Color Class Domination Partition. A proper color partition of G is called a Global Color Class Domination Partition if every color class is dominated by a vertex and each color class is independent of a vertex outside the class. The minimum cardinality of a Global Color Class Domination Partition is called the Global Color Class Domination Partition Number of G and is denoted by gcd G . In this paper a study of this new parameter is initiated and its relationships with other parameters are investigated.

Keywords

• Color class domination partition,Global color class domination partition,Dominator color class partition,Global color class domination number.

References

1. Chitra, S., (2012), Studies in Coloring in Graph with Special Reference to Color Class Domination, Ph.D. Thesis, M.K. University.
2. Chitra, S., Gokilamani and Swaminathan, V., (2010), Color Class Domination in Graphs, Mathematical and Experimental Physics edited by S. Jayalakshmi et. al., Narosa Publishing House.
3. Gera, R., (2007), On Dominator Coloring in Graphs, Graph Theory Notes, N.Y., 52, pp. 25–30.
4. Gera, R., Horton, S., and Rasmussen, C., (2006), Dominator Colorings and Safe Clique Partitions, Congr. Num. 181, pp. 19–32.