An improvement on the maximum number of k-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...

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 the Maximum Number of Dominating Classes in Graph Coloring

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

Bounds on the maximum number of minimum dominating sets

On maximum number of minimal dominating sets in graphs