  We establish exact sequences in $KK$-theory for graded relative Cuntz-Pimsner
algebras associated to nondegenerate $C^*$-correspondences. We use this to
calculate the graded $K$-theory and $K$-homology of relative Cuntz-Krieger
algebras of directed graphs for gradings induced by $\{0,1\}$-valued labellings
of their edge sets.
