On -domination in graphs

Abstract

Let be a graph and let be a family of subsets of such that A dominating set of is called an -dominating set if for all The minimum cardinality of an -dominating of is called the -domination number of and is denoted by In this paper we present several basic results on this parameter. We also introduce the concept of -irredundance and obtain an inequality chain four parameters.

Keywords

• domination
• -domination
• -domination number
• -irredundance