论文标题
关于寻找短路的光谱方法的评论
Remarks on the Spectral Approach to Finding Short Paths
论文作者
论文摘要
我们对一个一般问题感兴趣：与距离函数连接的图的光谱特性在多大程度上？我们的动机是斯坦纳伯格引起的这个问题的具体例子。我们通过图形族的构造提供了一些负面的结果，其中光谱属性以回答Steinerberger提出的许多问题的方式不同意距离函数。我们还通过用涉及图曲率的条件代替Steinerberger的设置来提供积极的结果。
We are interested in the general question: to what extent are the spectral properties of a graph connected to the distance function? Our motivation is a concrete example of this question that is due to Steinerberger. We provide some negative results via constructions of families of graphs where the spectral properties disagree with the distance function in a manner that answers many of the questions posed by Steinerberger. We also provide a positive result by replacing Steinerberger's set-up with conditions involving graph curvature.
