• DOI:10.1090/TRAN/8416
• Corpus ID: 220831359

Homological invariants of Cameron–Walker Graphs

@article{Hibi2020HomologicalIO,
  title={Homological invariants of Cameron–Walker Graphs},
  author={Takayuki Hibi and Hiroju Kanno and Kyouko Kimura and Kazunori Matsuda and Adam Van Tuyl},
  journal={arXiv: Commutative Algebra},
  year={2020}
}

• T. Hibi, Hiroju Kanno, +2 authors Adam Van Tuyl
• Published 28 July 2020
• Mathematics
• arXiv: Commutative Algebra

Let $G$ be a finite simple connected graph on $[n]$ and $R = K[x_1, \ldots, x_n]$ the polynomial ring in $n$ variables over a field $K$. The edge ideal of $G$ is the ideal $I(G)$ of $R$ which is generated by those monomials $x_ix_j$ for which $\{i, j\}$ is an edge of $G$. In the present paper, the possible tuples $(n, {\rm depth} (R/I(G)), {\rm reg} (R/I(G)), \dim R/I(G), {\rm deg} \ h(R/I(G)))$, where ${\rm deg} \ h(R/I(G))$ is the degree of the $h$-polynomial of $R/I(G)$, arising from Cameron--Walker graphs on $[n]$ will be completely determined.