Independence多项式与蝌蚪图的弱Lefschetz性质
Independence polynomials and the weak Lefschetz property for tadpole graphs
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中文总结 AI 辅助
本文证明蝌蚪图的独立多项式单峰并给出众数界，且分类了其边理想代数具有弱Lefschetz性质的参数对。
中文摘要 AI 辅助
设$T_{m,n}$为通过一条桥将圈$C_m$连接到路径$P_n$上所得的蝌蚪图。我们证明每个蝌蚪图的独立多项式是单峰的，并建立其众数的精确界。单峰性结果源于一个关于将路径附加到固定顶点所得图的一般准则。在特征为零的域上，我们还给出了由$T_{m,n}$的边理想与所有变量的平方所定义的Artinian代数具有弱Lefschetz性质的配对$(m,n)$的完全分类。
英文摘要
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.
发表机构
- University of Education, Hue University（顺化大学教育学院）
机构由 AI 辅助整理，请以论文原文为准。
