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DTSTART:20230101T000000
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DTSTART;TZID=America/Monterrey:20230525T130000
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CREATED:20230731T231638Z
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UID:7449-1685019600-1685025000@www.iimas.unam.mx
SUMMARY:Eigenvectors of graph Laplacians: a landscape
DESCRIPTION:Coloquio de Matemáticas Aplicadas\nWe review the properties of eigenvectors for the graph Laplacian matrix\, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. We focus on eigenvectors that have zero components and extend the pioneering results of Merris (1998) on graph transformations that preserve a given eigenvalue $\lambda$ or shift it\nin a simple way. These transformations enable us to obtain eigenvalues/vectors combinatorially instead of numerically; in particular we show that graphs having eigenvalues $\lambda= 1\,2\,\dots\,6$ up to six vertices can be obtained from a short list of graphs. For the converse problem of a subgraph $G$ of a graph $G”$\, both affording $\lambda$\, we prove results and conjecture that $G$ and $G”$ are connected by two of the simple transformations described above. \nImparte\nProf. Jean-Guy Caputo\nEngineering Mathematics Department\,\nINSA de Rouen Technical University
URL:https://www.iimas.unam.mx/event/eigenvectors-of-graph-laplacians-a-landscape/
LOCATION:Salón 203 del Edificio Anexo del IIMAS\, Circuito Escolar S/N\, Ciudad Universitaria\,\, Ciudad de México\, Coyoacán\, 04510\, Mexico
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