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2019 Regularity of powers of edge ideals of unicyclic graphs
Ali Alilooee, Selvi Kara Beyarslan, S. Selvaraja
Rocky Mountain J. Math. 49(3): 699-728 (2019). DOI: 10.1216/RMJ-2019-49-3-699

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 $2s+\DeclareMathOperator{reg} (I(G))-2$. We also give a combinatorial characterization of unicyclic graphs with regularity $\nu (G)+1$ and $\nu (G)+2$, where $\nu (G)$ denotes the induced matching number of $G$.

Citation

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Ali Alilooee. Selvi Kara Beyarslan. S. Selvaraja. "Regularity of powers of edge ideals of unicyclic graphs." Rocky Mountain J. Math. 49 (3) 699 - 728, 2019. https://doi.org/10.1216/RMJ-2019-49-3-699

Information

Published: 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07088332
MathSciNet: MR3983296
Digital Object Identifier: 10.1216/RMJ-2019-49-3-699

Subjects:
Primary: 05C25, 05C38, 05E40, 13D02, 13F20

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 3 • 2019
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