  Khovanov homology for knots has generated a flurry of activity in the
topology community. This paper studies the Khovanov type cohomology for graphs
with a special attention to torsions. When the underlying algebra is
$\mathbb{Z}[x]/(x^2)$, we determine precisely those graphs whose cohomology
contains torsion. For a larger class of algebras, we show that torsion often
occurs. Our investigation of torsion led to other related general results. The
ideas of this paper could potentially be used to predict the Khovanov-Rozansky
$sl(m)$ homology of knots (in particular $(2,n)$ torus knots). We also predict
that our work is connected with Hochschild and Connes cyclic homology of
algebras.
