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Turkish Journal of Mathematics

DOI

10.3906/mat-1507-109

Abstract

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 $\mathcal {SQ}$, 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.

First Page

1102

Last Page

1109

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