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

Abstract

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∘hn 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.