On the Number of Minimum Total Dominating Sets in Trees
The minimum total dominating set (MTDS) of a graph is a vertex subset D of
minimum cardinality such that every vertex of the graph is adjacent to at least one vertex of D.
In this paper we obtain a sharp upper bound for the number of MTDSs in the class
of n-vertex 2-caterpillars. We also show that for all n ≥ 1 every n-vertex tree has less than (√2)^n MTDSs.