Turkish Journal of Mathematics
DOI
10.3906/mat-1510-121
Abstract
Let $k\geq 3$ and $G=\theta_{n_1,\ldots, n_k}$ be a graph consisting of $k$ paths that have common endpoints. In this paper, we show that the projective dimension of $R/I(G)$ equals $bight I(G)$ or $ bight I(G)+1$. For some special cases, we explain $depth(R/I(G))$ in terms of invariants of graphs. Moreover, we prove the regularity of $R/I(G)$ equals $c_G$ or $c_G+1$, where $c_G$ is the maximum number of 3-disjoint edges in $G$.
First Page
320
Last Page
338
Recommended Citation
SEYYEDI, SEYYEDE MASOOME and RAHMATI, FARHAD
(2018)
"Regularity and projective dimension of the edge ideal of a generalized theta graph,"
Turkish Journal of Mathematics: Vol. 42:
No.
1, Article 27.
https://doi.org/10.3906/mat-1510-121
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss1/27
