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Spectra of graphs : theory and application
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The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.Abstract:
Introduction. Basic Concepts of the Spectrum of a Graph. Operations on Graphs and the Resulting Spectra. Relations Between Spectral and Structural Properties of Graphs. The Divisor of a Graph. The Spectrum and the Group of Automorphisms. Characterization of Graphs by Means of Spectra. Spectra Techniques in Graph Theory and Combinatories. Applications in Chemistry an Physics. Some Additional Results. Appendix. Tables of Graph Spectra Biblgraphy. Index of Symbols. Index of Names. Subject Index.read more
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Book ChapterDOI
Introduction to Graph Signal Processing
TL;DR: Spectral analysis of graphs is discussed next and some simple forms of processing signal on graphs, like filtering in the vertex and spectral domain, subsampling and interpolation, are given.
Journal ArticleDOI
On the second largest Laplacian eigenvalues of graphs
TL;DR: The second largest Laplacian eigenvalue of a graph is the second largest eigen value of the associated matrix as discussed by the authors, and it is shown in this paper that the extremal graph with maximum and the second maximum L 1 -separator of a connected graph can be characterized.
Journal ArticleDOI
Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph
Mustapha Aouchiche,F. K. Bell,Dragoš Cvetković,Pierre Hansen,Peter Rowlinson,Slobodan K. Simić,Dragan Stevanović +6 more
TL;DR: Three of the conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph are formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search.
Journal ArticleDOI
Spectral properties of the Laplacian on bond-percolation graphs
Werner Kirsch,Peter E. Müller +1 more
TL;DR: In this paper, it was shown that the Lifshits tail for the Dirichlet (Neumann) Laplacian at the lower (upper) spectral edge is at most 1/2, and thus depends on the spatial dimension.
Journal ArticleDOI
Motion synchronization in unmanned aircrafts formation control with communication delays
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