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