On the Number ofk-Dominating Independent Sets

On the Number of k-Dominating Independent Sets

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 kdominating independent sets in n-vertex graphs is bet...

The Number of Independent Dominating Sets of Labeled Trees

We count the numbers of independent dominating sets of rooted labeled trees, ordinary labeled trees, and recursive trees, respectively.

on the number of maximum independent sets of graphs

let $g$ be a simple graph. an independent set is a set ofpairwise non-adjacent vertices. the number of vertices in a maximum independent set of $g$ isdenoted by $alpha(g)$. in this paper, we characterize graphs $g$ with $n$ vertices and with maximumnumber of maximum independent sets provided that $alpha(g)leq 2$ or $alpha(g)geq n-3$.

On Dominating Sets And Independent Sets Of Graphs

A k-dominating set is a set D k V such that every vertex i 2 V nD k has at least k i neighbours in D k. The k-domination number k (G) of G is the cardinality of a smallest k-dominating set of G. For k 1 = ::: = k n = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an upper bound for the domination number found then the conception of k-domina...

Bounds on the maximum number of minimum dominating sets