We study the existence and the number of k‐dominating independent sets in certain graph
families. While the case namely the case of maximal independent sets—which is originated
from Erdős and Moser—is widely investigated, much less is known in general. In this paper
we settle the question for trees and prove that the maximum number of k‐dominating
independent sets in n‐vertex graphs is between and if, moreover the maximum number of 2‐
dominating independent sets in n‐vertex graphs is between and. Graph constructions …

We study the existence and the number of $ k $-dominating independent sets in certain
graph families. While the case $ k= 1$ namely the case of maximal independent sets-which
is originated from Erdős and Moser-is widely investigated, much less is known in general. In
this paper we settle the question for trees and prove that the maximum number of $ k $-
dominating independent sets in $ n $-vertex graphs is between $ c_k\cdot\sqrt [2k]{2}^ n $
and $ c_k'\cdot\sqrt [k+ 1]{2}^ n $ if $ k\geq 2$, moreover the maximum number of $2 …