Acta Mathematica Vietnamica
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The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles
Hop D. Nguyen
,
Quang Hoa Tran
Abstract
Given a base field $\Bbbk$ of characteristic zero, for each graph $G$, we associate the artinian algebra $A(G)$ defined by the edge ideal of $G$ and the squares of the variables. We study the weak Lefschetz property of $A(G)$. We classify some classes of graphs with relatively few edges, including paths and cycles, such that its associated artinian ring has the weak Lefschetz property.