Size of nodal domains of the eigenvectors of a graph
Size of nodal domains of the eigenvectors of a graph
复制标题
图的特征向量的节点域的大小
DOI：
10.1002/rsa.20925
复制
发表时间：
2020
影响因子：
1
通讯作者：
Rudelson, Mark
中科院分区：
文献类型：
--
作者：
Huang, Han;Rudelson, Mark
考虑aG（n，p）图的邻接矩阵的一个特征向量.节点域是顶点集的连通分量，其中该特征向量具有常数符号。我们知道，对于一个非前导特征值对应的特征向量，有两个节点域的概率很高。我们证明，以高概率，这些节点域的大小是近似相等的。
Consider an eigenvector of the adjacency matrix of aG(n,p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other.