Turkish Journal of Mathematics
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 $G$.
DOI
10.3906/mat-1510-121
Keywords
Big height, projective dimension, regularity, depth
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
