On the Existence of Independent [ j , k ]-Dominating Sets in the Generalized Corona of Graphs.

In 2013 the concept of [ j , k ] -dominating sets in graphs have been introduced as an extension of [ 1 , k ] -dominating sets. Regarding studying [ j , k ] -dominating sets, the research is also interesting if the additional independence requirement is assumed, because the existence of independent [ 1 , k ] -dominating sets is an NP -complete problem in general case. Inspired by this topic, in this paper we study the problem of the existence of independent [ j , k ] -dominating sets in a special, multi-argument graph product. We give the complete characterization of the generalized corona G ∘ h n with an independent [ j , k ] -dominating set, for arbitrary positive integers j and k, which generalize the known result for a corona of two graphs. [ABSTRACT FROM AUTHOR]