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.
Keywords
Castelnuovo-Mumford regularity, edge ideal, induced matching, projective dimension, well-covered graph
First Page
1102
Last Page
1109
Recommended Citation
LASHANI, ESFANDIYAR and JAHAN, ALI SOLEYMAN
(2016)
"Regularity and projective dimension of some class of well-covered graphs,"
Turkish Journal of Mathematics: Vol. 40:
No.
5, Article 15.
https://doi.org/10.3906/mat-1507-109
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss5/15
