arXiv subjects

Nguyen Duy Phuoc

Publications and source records attributed to Nguyen Duy Phuoc.

3 recordsLinked to original sources

arXiv2026

Independence polynomials and the weak Lefschetz property for tadpole graphs

Let $T_{m,n}$ be the tadpole graph obtained by joining a cycle $C_m$ to a path $P_n$ by a bridge. We prove that the independence polynomial of every tadpole graph is unimodal and establish sharp bounds for its mode. The unimodality result follows from a general criterion for graphs obtained by attaching a path to a fixed vertex. Over a field of characteristic zero, we also give a complete classification of the pairs $(m,n)$ for which the Artinian algebra defined by the edge ideal of $T_{m,n}$ together with the squares of all variables has the weak Lefschetz property.

math.AC↗

arXiv2025

The Weak Lefschetz Property for Tensor Products of Artinian Monomial Algebras and Its Applications to Lollipop Graphs

In this paper, we investigate the weak Lefschetz property for tensor products of Artinian monomial algebras and complete quadratic monomial algebras. As an application, we classify the weak Lefschetz property of the Artinian algebras $A(L_{m,n})$, which are defined by the edge ideals of the lollipop graphs $L_{m,n}$ together with the squares of the variables.

math.AC↗

arXiv2024

The weak Lefschetz properties of artinian monomial algebras associated to certain tadpole graphs

Given a simple graph $G$, the artinian monomial algebra associated to $G$, denoted by $A(G)$, is defined by the edge ideal of $G$ and the squares of the variables. In this article, we classify some tadpole graphs $G$ for which $A(G)$ has or fails the weak Lefschetz property.

math.AC↗