论文标题
用完全积极的半决赛$ q $ - matrices表征图表
Characterizing graphs with fully positive semidefinite $Q$-matrices
论文作者
论文摘要
对于$ q \ in \ mathbb {r} $，$ q $ -matrix $ q = q_q $的q_q $的简单graph $ g =（v，e）$ as $ q_q =（q^{\ partial（x，y）}）_ {x，x，y \ in v} $ parte $ \ p path the path-the path-the path-Lentta。描述$ q \ in \ mathbb {r} $组成的集合$π（g）$，从量子概率理论的角度来看，$ q_q $是$ q_q $的$ q_q $是正的半光谱分析。假设$ g $至少有两个顶点。然后很容易看出$π（g）$是间隔$ [-1,1] $的非空封闭子集。在本说明中，我们表明$π（g）= [-1,1] $，并且仅当$ g $等于等同于同一嵌入到hypercube（如果$ g $是无限的（如果$ g $是无限））中，则仅当$ g $是双方的，并且没有某些五个Vertex的配置，并且具有某些五个Vertex的示例，该示例是某些五个Vertex的示例，该示例是$ k__________________________________________________3.2,3,3,3,3,3,3,3,3,2,3,2,3,2,3,3 r。
For $q\in\mathbb{R}$, the $Q$-matrix $Q=Q_q$ of a connected simple graph $G=(V,E)$ is $Q_q=(q^{\partial(x,y)})_{x,y\in V}$, where $\partial$ denotes the path-length distance. Describing the set $π(G)$ consisting of those $q\in \mathbb{R}$ for which $Q_q$ is positive semidefinite is fundamental in asymptotic spectral analysis of graphs from the viewpoint of quantum probability theory. Assume that $G$ has at least two vertices. Then $π(G)$ is easily seen to be a nonempty closed subset of the interval $[-1,1]$. In this note, we show that $π(G)=[-1,1]$ if and only if $G$ is isometrically embeddable into a hypercube (infinite-dimensional if $G$ is infinite) if and only if $G$ is bipartite and does not possess certain five-vertex configurations, an example of which is an induced $K_{2,3}$.
