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Fakultät für Mathematik
Fakultät für Mathematik
E. M.Borba, U. Schwerdtfeger, S. Richter: Non-linear Generalizations of eigenvalues of Graph Laplacians and Algebraic Connectivity

E. M.Borba, U. Schwerdtfeger, S. Richter: Non-linear Generalizations of eigenvalues of Graph Laplacians and Algebraic Connectivity


Author(s):
E. M.Borba
U. Schwerdtfeger
S. Richter
Title:
E. M.Borba, U. Schwerdtfeger, S. Richter: Non-linear Generalizations of eigenvalues of Graph Laplacians and Algebraic Connectivity
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 06, 2017
Mathematics Subject Classification:
    05C50 []
    05C40 []
    15A18 []
    47J10 []
Abstract:
We generalize the notion of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian matrix, by varying the norms in the Rayleigh-Ritz characterization. The so obtained parameters are shown to be well-defined and to be the least non-zero eigenvalues of the corresponding non-linear eigenvalue problem whenever the graph is connected. We provide combinatorial interpretations of several non-smooth cases.
Keywords:
(signless) p-Laplacian, algebraic connectivity, isoperimetric number, Rayleigh quotient, graph partition, nonlinear eigenvalue problem
Language:
English
Publication time:
12/2017

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