Enumerating minimal dominating sets in chordal graphs

The maximum number of minimal dominating sets in a chordal graph on n vertices is known to be at most 1.6181n. However, no example of a chordal graph with more than 1.4422n minimal dominating sets is known. In this paper, we narrow this gap between the known upper and lower bounds by showing that the maximum number of minimal dominating sets in a chordal graph is at most 1.5214n.