We propose the conjecture that every tree with order n at least 2 and
total domination number γt has at most
(2γtn−2γt)2γt
minimum total dominating sets. As a relaxation of this conjecture, we show that
every forest F with order n, no isolated vertex, and total domination
number γt has at most min{(8e)γt(2γtn−2γt)2γt,(1+2)n−γt,1.4865n} minimum total dominating sets