Publications - Published papers
Please find below publications of our group. Currently, we list 565 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (
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) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.
Graph Laplacians, Nodal Domains, and Hyperplane Arrangements
Türker Biyikoglu, Wim Hordijk, Josef Leydold, Tomaz Pisanski, and Peter F. Stadler
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Status: Published
Linear algebra appl. Volume 390, pp. 155-174, 2004. ISSN 0024-3795
Abstract
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 ψ 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 ψ 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 information is available, the computations are still non-trivial. Nevertheless, we obtained some new results and a number of conjectures.
Keywords
Graph Laplacian, Hyperplane Arrangement, Nodal Domains, Landscapes
Note
Alternative Numbers: SFI 02-09-046