Year: 2017
Type: preprint
Abstract: Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a unicyclic graph then for all $s \geq 1$ the regularity of $I(G)^s$ is exactly $2s+\text{reg}(I(G))-2$. We also characterize the unicyclic graphs with regularity $ν(G)+1$ and $ν(G)+2$, where $ν(G)$ denotes the induced matching number of $G$.
Source: arXiv (Cornell University)
Authors: Alilooee, Ali, Kara, Selvi, Selvaraja, S.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2593480634