Bounds on the maximum number of minimum dominating sets

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

Bounds on the Maximum Number

Counting Minimum Weighted Dominating Sets

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