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

Graphs with extremal energy should have a small number of distinct eigenvaluesD. Cvetkovic and J. GroutFaculty of Electrical Engineering, University of Belgrade, P.O.Box 35–54, 11120 Belgrade, SerbiaDepartment 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 Full text of the article: (for faster download, first choose a mirror)
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
