A NOTE ON NON-DOMINATING SET PARTITIONS IN GRAPHS

作者：Desormeaux Wyatt J^*; Haynes Teresa W; Henning Michael A

来源：Discussiones Mathematicae - Graph Theory, 2016, 36(4): 1043-1050.

DOI：10.7151/dmgt.1895

• domination
• total domination
• non-dominating partition
• non-total dominating partition

A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S. The cardinality of a minimum dominating (total dominating) set of G is called the domination (total domination) number. A set that does not dominate (totally dominate) G is called a non dominating (non-total dominating) set of G. A partition of the vertices of G into non-dominating (non-total dominating) sets is a non-dominating (non total dominating) set partition. We show that the minimum number of sets in a non-dominating set partition of a graph G equals the total domination number of its complement (G) over bar and the minimum number of sets in a non-total dominating set partition of G equals the domination number of (G) over bar. This perspective yields new upper bounds on the domination and total domination numbers. We motivate the study of these concepts with a social network application.

• 出版日期2016-11