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, S. M, & RAHMATI, F (2018). Regularity and projective dimension of the edge ideal of a generalized theta graph. Turkish Journal of Mathematics 42 (1): 320-338. https://doi.org/10.3906/mat-1510-121
