We show that the binomial tree topology is well suited for scalable
deterministic and robust group management by exhibiting efficient procedures
for decentralized construction, replacement of failed elements and routing.
Concerning particularly the communication criteria, we address the conjecture
which says that the binomial tree is the spanning tree of the hypercube with
minimum mean distance between nodes. More precisely, we exhibit a class of
transformations which can be used to prove the conjecture for small values of
n and for which the binomial tree is a local minimum for all values of n.