On the maximum number of minimum dominating sets in forests

Bounds on the maximum number of minimum dominating sets

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].  

On maximum number of minimal dominating sets in graphs

The Maximum Number of Maximal Independent Sets in Forests

Let G be a simple and undirected graph. By mi(G) we denote the number of maximal independent sets in G. In this note, we determine the maximum number of maximal independent sets among the set of a type of forests. Mathematics Subject Classification: 05C05; 05C50; 05C69

Counting Minimum Weighted Dominating Sets

We show how to count all minimumweighted dominating sets of a graph on n vertices in timeO(1.5535).