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In this paper we study the Castelnuovo{Mumf 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{Mumf ord 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

Regularity and projective dimension of some class of well-covered graphs