可分层图

与某些蝌蚪图相关的阿廷单项式代数的弱莱夫谢茨性质

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

该研究围绕与简单图相关的阿廷单项式代数$A(G)$的弱莱夫谢茨性质展开，对部分满足或不满足该性质的蝌蚪图进行了分类，推进了相关代数性质的图类刻画研究。

On the socle of Artinian algebras associated to graphs

Given a simple graph, consider the polynomial ring with coefficients in a field and variables identified with the edges of the graph. Given a non-empty even cardinality Eulerian subgraph and a choice of half of its edges, consider the homogeneous binomial obtained by taking the product of these edges minus the product of the remaining edges of the subgraph. We define a homogeneous ideal by taking as generators all binomials obtained in this way, varying the Eulerian subgraph and the choice of half of its edges, together with the squares of the variables of the ring. This ideal is related to th…

与路径和圈相关的阿廷代数的弱莱夫谢茨性质

The weak Lefschetz property of artinian algebras associated to paths and cycles

本文研究由图边理想和变量平方定义的阿廷代数的弱莱夫谢茨性质，并对边数较少的图类（包括路径和圈）进行了分类。

与图相关的顶点覆盖 Artinian 代数的弱和强 Lefschetz 性质

Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs

本文证明当最小顶点覆盖大小超过顶点数一半时，与图覆盖理想相关的 Artinian 代数具有弱 Lefschetz 性质，并分类了临界情形下路径、圈、Ferrers 图和良覆盖树的 WLP。

On the problem of the finiteness of the compressed zero divisor graphs of Artinian rings

Let R be an Artinian ring and G be the compressed zero-divisor graph associated to R. The question of when the clique number of compressed zero-divisor graphs is finite was raised by J. Coykendall, S. Sather-Wagstaff, L. Sheppardson, and S. Spiroff, in their survey paper entitled On Zero-divisor Graphs. They proved that if length of R is at most four then the clique number is finite. In the length six case they gave an example of a ring where the clique is infinite. In this paper we show that when length of ring is five then the clique number of compressed zero-divisor graph is finite.

On the nonorientable genus of the generalized unit and unitary Cayley graphs of a commutative ring

Let $R$ be a commutative ring and let $U(R)$ be multiplicative group of unit elements of $R$. In 2012, Khashyarmanesh et al. defined generalized unit and unitary Cayley graph, $Γ(R, G, S)$, corresponding to a multiplicative subgroup $G$ of $U(R)$ and a non-empty subset $S$ of $G$ with $S^{-1}=\{s^{-1} \mid s\in S\}\subseteq S$, as the graph with vertex set $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $s\in S$ such that $x+sy \in G$. In this paper, we characterize all Artinian rings $R$ whose $Γ(R,U(R), S)$ is projective. This leads to determine all Artinia…