Quotation Leydold, Josef. 2009. Extremal graphs with minimal k-th Laplacian eigenvalue. 24th LL-Seminar on Graph Theory, Leoben, Österreich, 254.04.-25.04..


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Abstract

A method for characterizing graphs that have smallest (or largest) Laplacian eigenvalue within a particular class of graphs works as following: Take a Perron vector, rearrange the edges of the graph and compare the respective Rayleigh quotients. By the Rayleigh-Ritz Theorem we can draw some conclusions about the change of the smallest eigenvalue. This approach, however, does not work for the k-th Laplacian eigenvalue, as now we have to use the Courant-Fisher Theorem that involves minimization of the Rayleigh quotients with respect to constraints that are hard to control. In this talk we show that sometimes we can get local properties of extremal graphs by means of the concept of "geometric nodal domains" and "Dirichlet matrices". This is in particular the case for the algebraic connectivity.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Paper presented at an academic conference or symposium
Language English
Title Extremal graphs with minimal k-th Laplacian eigenvalue
Event 24th LL-Seminar on Graph Theory
Year 2009
Date 254.04.-25.04.
Country Austria
Location Leoben
URL http://conferences.imfm.si/conferenceDisplay.py?confId=22

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Leydold, Josef (Details)
Organization
Institute for Statistics and Mathematics IN (Details)
Research Institute for Computational Methods FI (Details)
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