A Fiedler-like theory for the perturbed Laplacian

Title:

A Fiedler-like theory for the perturbed Laplacian

Creator:

Rocha, Israel and Trevisan, Vilmar

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a347ed66-4ae4-417a-a08d-e0a4f8223957
uuid:a347ed66-4ae4-417a-a08d-e0a4f8223957
issn:0011-4642

Subject:

matematika, mathematics, perturbed Laplacian matrix, Fiedler vector, algebraic connectivity, graph partitioning, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

The perturbed Laplacian matrix of a graph G is defined as DL = D−A, where D is any diagonal matrix and A is a weighted adjacency matrix of G. We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use the notion of Perron component for the perturbed Laplacian matrix of a graph and show how its second smallest eigenvalue can be characterized using this definition., Israel Rocha, Vilmar Trevisan., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

717-735

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:3

Harvested from:

CDK

Metadata only:

false