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

Authors : Esfandiyar LASHANI, Ali Soleyman JAHAN

Pages : 1102-1109

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Publication Date : 0000-00-00

Article Type : Research Paper

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 $R/Iinsert ignore into journalissuearticles values(G);$ will be equal to induced matching number of $G$. For this class of graphs we also compute the projective dimension of the ring $R/Iinsert ignore into journalissuearticles values(G);$. As a corollary we describe these invariants in well-covered forests, well-covered chordal graphs, Cohen-Macaulay Cameron-Walker graphs, and simplicial graphs.
Keywords : Castelnuovo Mumford regularity, edge ideal, induced matching, projective dimension, well covered graph