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原文連結
論文資訊
- 類型：已發表論文
- 日期：2004
摘要
Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. Here we investigate their so-called nodal domains, i.e. the connected components of the maximal induced subgraphs of G on which an eigenvector psi does not change sign. An analogue of Courant's nodal domain theorem provides upper bounds on the number of nodal domains depending on the location of psi in the spectrum. This bound, however, is not sharp in general. In this contribution we consider the problem of computing minimal and maximal numbers of nodal domains for a particular graph. The class of Boolean Hypercubes is discussed in detail. We find that, despite the simplicity of this graph class, for which complete spectral 資訊 is available, the computations are still non-trivial. Nevertheless
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