  We compute the Betti numbers for all the powers of initial and final
lexsegment edge ideals. For the powers of the edge ideal of an anti-$d-$path,
we prove that they have linear quotients and we characterize the normally
torsion-free ideals. We determine a class of non-squarefree ideals, arising
from some particular graphs, which are normally torsion-free.

Commutative Algebra;Combinatorics