  Let X be an algebraic toric set in a projective space over a finite field. We
study the vanishing ideal, I(X), of X and show some useful degree bounds for a
minimal set of generators of I(X). We give an explicit description of a set of
generators of I(X), when X is the algebraic toric set associated to an even
cycle or to a connected bipartite graph with pairwise disjoint even cycles. In
this case, a fomula for the regularity of I(X) is given. We show an upper bound
for this invariant, when X is associated to a (not necessarily connected)
bipartite graph. The upper bound is sharp if the graph is connected. We are
able to show a formula for the length of the parameterized linear code
associated with any graph, in terms of the number of bipartite and
non-bipartite components.
