  In the context of a model of space-time foam, made by $N$ wormholes we
discuss the possibility of having a foam formed by different configurations. An
equivalence between Schwarzschild and Schwarzschild-Anti-de Sitter wormholes in
terms of Casimir energy is shown. An argument to discriminate which
configuration could represent a foamy vacuum coming from Schwarzschild black
hole transition frequencies is used. The case of a positive cosmological
constant is also discussed. Finally, a discussion involving charged wormholes
leads to the conclusion that they cannot be used to represent a ground state of
the foamy type.
