  In this paper, we explain the regularity, projective dimension and depth of
edge ideal of some classes of graphs in terms of invariants of graphs. We show
that for a $C_5$-free vertex decomposable graph $G$, $\T{reg}(R/I(G))= c_G$,
where $c_G$ is the maximum number of 3-disjoint edges in $G$. Moreover for this
class of graphs we characterize $\T{pd}(R/I(G))$ and $\T{depth}(R/I(G))$. As a
corollary we describe these invariants in forests and sequentially
Cohen-Macaulay bipartite graphs.
