Sign-changing diagonal perturbations of Laplacian matrices of graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43931899" target="_blank" >RIV/49777513:23520/17:43931899 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.laa.2017.05.043" target="_blank" >https://doi.org/10.1016/j.laa.2017.05.043</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2017.05.043" target="_blank" >10.1016/j.laa.2017.05.043</a>

Result language
angličtina
Original language name
Sign-changing diagonal perturbations of Laplacian matrices of graphs
Original language description
In this paper we provide sufficient conditions for positive (semi)definiteness of sign-changing diagonal perturbations of positive semidefinite difference operators and their matrix representations, the Laplacian matrices of graphs. Our estimates arise from the discrete version of the Poincar'{e} inequality and essentially depend on the algebraic connectivity of the underlying graph, i.e., the second smallest eigenvalue of the graph Laplacian matrix. We generalize our results to positive semidefinite matrices with simple zero eigenvalue and illustrate our results by numerical experiments and discuss the optimality of our assumptions.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-07690S" target="_blank" >GA15-07690S: Partial Difference and Differential Equations on Lattices</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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