Help:=proc(): print(`V(A,k)`): end:


#V(A,k): all the k-letter words in the alphabet A
V:=proc(A,k) local V1:
if k=0 then
  RETURN({[]}):
fi:

V1:=V(A,k-1):

 {seq(seq([op(V1[i]), A[j]],j=1..nops(A)),i=1..nops(V1))}:

end:


#G(A,k): given an alphabet A and a pos. integer k
#constructs the graph [V,E] whose set of vertices V
#are all the k-letter words in A, and [u,v] is
#an edge iff op(2..k,u)=op(1..k-1,v)
#
G:=proc(A,k) local V1,E1,i,j,v1:
V1:=V(A,k):
E1:={}:

for i from 1 to nops(V1) do
v1:=V1[i]:

E1:=E1 union {seq([v1, [op(2..k,v1),A[j]]],j=1..nops(A))}:

od:

[V1,E1]:

end: