论文标题
单周期图的高序光谱表征
High-ordered spectral characterization of unicyclic graphs
论文作者
论文摘要
在本文中，我们将应用张量及其痕迹来研究独立图的光谱表征。令$ g $为图，$ g^m $是$ g $的$ m $ th Power（HyperGraph）。 $ g $的光谱指的是其邻接矩阵，$ g^m $的光谱指的是其邻接张量。图形$ g $被称为高序光谱（简称DHS）确定，如果$ h $是一张图，以至于$ h^m $是coseptral，cospectral th $ g^m $，所有$ m $，则$ h $是同构至$ g $。在本文中，我们首先给出公式的单车图轨迹，然后提供一些统一图的高序圆环不变式。我们证明，一类带有共光序列的独立图是DHS，并给出了两个无限多对骑镜的独立图的示例，但具有不同的高序光谱。
In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let $G$ be a graph and $G^m$ be the $m$-th power (hypergraph) of $G$. The spectrum of $G$ is referring to its adjacency matrix, and the spectrum of $G^m$ is referring to its adjacency tensor. The graph $G$ is called determined by high-ordered spectra (DHS for short) if, whenever $H$ is a graph such that $H^m$ is cospectral with $G^m$ for all $m$, then $H$ is isomorphic to $G$. In this paper we first give formulas for the traces of the power of unicyclic graphs, and then provide some high-ordered cospectral invariants of unicyclic graphs. We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of infinitely many pairs of cospectral unicyclic graphs but with different high-ordered spectra.
