Graph Laplacians and topology
Graph Laplacians and topology
复制标题
图拉普拉斯算子和拓扑
DOI：
10.1007/s11512-007-0059-4
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
P. Kurasov
中科院分区：
文献类型：
--
作者：
P. Kurasov
考虑度量图上的拉普拉斯算子。证明了紧图的拉普拉斯算子的谱决定图的总长度、连通分支数和欧拉特征线。对于一类非紧图，由离散特征值和散射矩阵组成的散射数据决定了其相同的特征。
Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same characteristics are determined by the scattering data consisting of the scattering matrix and the discrete eigenvalues.