GLOBAL COLOR CLASS DOMINATION PARTITION OF A GRAPH

• Published in: TWMS journal of applied and engineering mathematics Vol. 9; no. 3; p. 681
• Main Authors: Praba, V, Swaminathan, V
• Format: Journal Article
• Language: English
• Published: Istanbul Turkic World Mathematical Society 01.01.2019; Elman Hasanoglu
• Subjects: Graph coloring; Graph theory; Mathematical research; Parameters; Partitions (mathematics); India
• ISSN: 2146-1147; 2146-1147

Color class domination partition was suggested by E. Sampathkumar and it was studied in [1]. A proper color partition of a finite, 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 different 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 [[chi].sub.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. AMS Subject Classification: 05C69