图的加倍常数与spectral theory
Doubling constants and spectral theory on graphs
摘要：
研究了在有限或无限图$G$上定义的所有可能的加倍测度中的最小加倍常数。我们表明，这个常数可以估计从下面的$1+ r(A_G)$，其中$r(A_G)$是谱半径的邻接矩阵的$G$，并研究当这两个数量一致。我们还说明了如何顺从的自同构群的图可以与寻找加倍极小。最后，我们在Smith图的基础上，给出了加倍常数小于3的图的一个完全刻画。
英文摘要：
We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph $G$. We show that this constant can be estimated from below by $1+ r(A_G)$, where $r(A_G)$ is the spectral radius of the adjacency matrix of $G$, and study when both quantities coincide. We also illustrate how amenability of the automorphism group of a graph can be related to finding doubling minimizers. Finally, we give a complete characterization of graphs with doubling constant smaller than 3, in the spirit of Smith graphs.
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