EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIV, No. 32, pp. 43–57 (2007)

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Graphs with extremal energy should have a small number of distinct eigenvalues

D. Cvetkovic and J. Grout

Faculty of Electrical Engineering, University of Belgrade, P.O.Box 35–54, 11120 Belgrade, Serbia
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA

Abstract: The sum of the absolute values of the eigenvalues of a graph is called the energy of the graph. We study the problem of finding graphs with extremal energy within specified classes of graphs. We develop tools for treating such problems and obtain some partial results. Using calculus, we show that an extremal graph "should" have a small number of distinct eigenvalues. However, we also present data that show in many cases that extremal graphs can have a large number of distinct eigenvalues.

Keywords: graph spectra , graph energy , Lagrange multipliers

Classification (MSC2000): 05C50

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Electronic fulltext finalized on: 23 Sep 2007. This page was last modified: 20 Jun 2011.

© 2007 Mathematical Institute of the Serbian Academy of Science and Arts
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