## Assumes labels are {1..n}.
PCpablo:=proc(T) local n,Lvs,i,v,P,N,V,L,nick,e:
 n:=nops(T)+1:
 V:= {seq(op(e), e in T)}:
 N:=table():
 for v in V do:
  N[v]:={}: 
 od:
 
 L:={}:
 
 # Find the neighbors of every vertex
 for e in T do:
  N[e[1]]:= N[e[1]] union {e[2]}:
  N[e[2]]:= N[e[2]] union {e[1]}:
 od:
 
 # Find all the leaves
 for v in V do:
  if nops(N[v])=1 then:
   L:= L union {v}:
  fi:
 od:



 P:=[-1$(n-2)]: # defined ahead of time to avoid the [ ,op] copying issue.
 for i from 1 to n-2 do:
  nick:=PC1(op(N),L): # current PC1 output
  P[i]:=nick[1]:

  # remove the smallest leaf from consideration:
  L:=L minus {nick[2]}:    
  N[nick[1]]:= N[nick[1]] minus {nick[2]}:
  N[nick[2]]:= {}:

  # Consider that nick[1] (neighbor) may now be a leaf
  if nops( N[nick[1]] ) = 1 then:
   L:=L union {nick[1]}:
  fi:
 od:

 P:
end: