A Note on the Maximum Number of Minimal Connected Dominating Sets in a Graph

Abstract

We prove constructively that the maximum possible number of minimal connected dominating sets in a connected undirected graph of order $n$ is in $\Omega (1.489^n)$. This improves the previously known lower bound of $\Omega (1.4422^n)$ and reduces the gap between lower and upper bounds for input-sensitive enumeration of minimal connected dominating sets in general graphs as well as some special graph classes.