论文标题
在阈值超图的光谱上
On the Spectra of Threshold Hypergraphs
论文作者
论文摘要
从一个孤立的顶点开始，在这里，我们通过反复添加孤立的顶点或$ k $的顶点集来构建阈值超图。我们通过一串非阴性整数表示阈值超图，并从其字符串表示中找到阈值超图的拉普拉斯频谱。我们还计算了从费雷勒的学位序列图中的某些阈值超图的完整拉普拉斯频谱。我们表明，对于某些$ r $的$ r $ integral，$ r $的积分倍数为$ r $，对于某些$ r \ in \ mathbb {q} $，$ r $ integral spectra是$ r $ integral。我们还构建了另一类的超图，其laplacian光谱是$ r $ ingertral。
Starting with an isolated vertex, here we construct a threshold hypergraph by repeatedly adding an isolated vertex or a $k$-dominating vertex set. We represent a threshold hypergraph by a string of non-negative integers and find the Laplacian spectrum of threshold hypergraphs from their string representation. We also compute the complete Laplacian spectrum of certain threshold hypergraphs from the Ferrer's diagram of their degree sequences. We show that the Laplacian spectra of threshold hypergraphs are $r$-integral, i.e., integral multiple of $r$, for some $r\in \mathbb{Q}$. We also construct another class of hypergraphs whose Laplacian spectra are $r$-integral.
