图的顶点扩张超图的谱矩与特征多项式
Spectral moments and characteristic polynomials of vertex expansion hypergraphs of graphs
- School of Mathematical Sciences, Harbin Engineering University（哈尔滨工程大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过$s$-倍闭游走刻画图的顶点扩张超图的谱矩，并由此推导其特征多项式。
AI中文摘要：
$s$-顶点扩张超图 $G^{[s]}$ 是将图 $G$ 的每个顶点替换为 $s$ 个新顶点而得到的 $2s$-一致超图。若 $G$ 中一条闭游走到达每个顶点的次数均能被 $s$ 整除，则称其为 $s$-倍闭游走。本文用 $G$ 中的 $s$-倍闭游走给出了 $G^{[s]}$ 的谱矩表达式，并利用这些谱矩给出了 $G^{[s]}$ 的特征多项式。
英文摘要：
The $s$-vertex expansion hypergraph $G^{[s]}$ is the $2s$-uniform hypergraph obtained by replacing each vertex of a graph $G$ with $s$ new vertices. A closed walk in $G$ is called an $s$-multiple closed walk if the number of times it arrives at each vertex of $G$ is divisible by $s$. In this paper, we obtain an expression for the spectral moments of $G^{[s]}$ in terms of $s$-multiple closed walks in $G$. Using these spectral moments, we give the characteristic polynomial of $G^{[s]}$.
