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arXiv · 1702.00916

Regularity of Powers of Unicyclic Graphs

Ali Alilooee·Selvi Kara·S. Selvaraja
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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 $G$.

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Ali Alilooee, Selvi Kara, S. Selvaraja. 2018-11-19. Regularity of Powers of Unicyclic Graphs. https://arxiv.org/abs/1702.00916

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