In this paper we study the Castelnuovo{Mumford regularity of an edge ideal associated with a graph in a special class of well-covered graphs. We show that if G belongs to the class SQ, then the Castelnuovo{Mumford regularity of R=I(G) will be equal to induced matching number of G. For this class of graphs we also compute the projective dimension of the ring R=I(G) . As a corollary we describe these invariants in well-covered forests, well-covered chordal graphs, Cohen{Macaulay Cameron{Walker graphs, and simplicial graphs.
