We propose the conjecture that every tree with order n at least 2 and
total domination number Ξ³tβ has at most
(2Ξ³tββnβ2Ξ³tβββ)2Ξ³tββ
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 Ξ³tβ has at most min{(8eβ)Ξ³tβ(2Ξ³tββnβ2Ξ³tβββ)2Ξ³tββ,(1+2β)nβΞ³tβ,1.4865n} minimum total dominating sets
We propose the conjecture that every tree with order n at least 2 and
total domination number Ξ³tβ has at most
(2Ξ³tββnβ2Ξ³tβββ)2Ξ³tββ
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 Ξ³tβ has at most min{(8eβ)Ξ³tβ(2Ξ³tββnβ2Ξ³tβββ)2Ξ³tββ,(1+2β)nβΞ³tβ,1.4865n} minimum total dominating sets