Vol. 6, No. 5, 2013
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Magnetic interpretation of the nodal defect on graphs

Yves Colin de Verdière
Vol. 6 (2013), No. 5, 1235–1242
DOI: 10.2140/apde.2013.6.1235
Abstract

We present a natural proof of a recent and surprising result of Gregory Berkolaiko interpreting the Courant nodal defect as a Morse index. This proof is inspired by a nice paper of Miroslav Fiedler published in 1975.

Keywords
operator on graphs, Schrödinger operators with magnetic fields, Morse index, Courant nodal theorem, Hill's operator
Mathematical Subject Classification 2010
Primary: 05C50, 35P05
Milestones
Received: 13 December 2012
Revised: 15 January 2013
Accepted: 14 February 2013
Published: 3 November 2013
Authors
Yves Colin de Verdière
Unité Mixte de Recherche CNRS-UJF 5582
Institut Fourier
BP 74
38402 Saint Martin d’Hères cedex
France
http://www-fourier.ujf-grenoble.fr/~ycolver/