need advice

[Wouter Meeussen]

concerning my last mail:
"trees : depth first or width first"

I'm looking for proper terminology, and some trivia-detection.

item 1.
Is it generally accepted to represent these trees by their binary form,
and to order them in decreasing numerical order?
Would an entry in EIS make sense to the "combinatorially literates" without 
explicit reference to this (natural?) ordering?

item 2.
In Mathematica's Combinatorica Package, a 'Breadth-First' and 'Depth-First' 
traversal of a Graph is documented. I take it (?) that the same terminology 
can be used here, and that these trees are a 'special kind' of directed 
graph of general interest (?).
It would be most surprising if such matters (1 on 1 correspondance between 
breadth-first and depth-first trees) would not have been published yet, so 
a nice literature reference would be nice (R.P. Stanley ??).

item 3.
Would it make sense to