## GLOBAL COLOR CLASS DOMINATION PARTITION OF A GRAPH

## *V. Praba, V. Swaminathan*

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## 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.