Description of a multiple binary-tree:
A multiple binary-tree network has n inputs and n outputs, where n is a power of 2. Each input is connected to the root of a binary tree with n/2 leaves and with edges pointing away from the root. Likewise, each output is connected to the root of a binary tree with n/2 leaves and with edges pointing toward the root.
Two edges point from each leaf of an input tree, and each of these edges points to a leaf of an output tree. The matching of leaf edges is arranged so that for every input and output tree, there is an edge from a leaf of the input tree to a leaf of the output tree, and every output tree leaf has exactly two edges pointing to it.
From this description, it is clear that the root, as well as the leaves of an input tree, has 1 incoming edge and 2 outgoing edges. On the other hand, the root and leaves of an output tree have 2 incoming edges and 1 outgoing edge. I am not able to figure out what should be the switch size of this network? Also, are N × M switches (where N ≠ M) possible in a communication network?