EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXIX, No. 29, pp. 85–102 (2004)

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Sets of cospectral graphs with least eigenvalue at least $-2$ and some related results

D. Cvetkovic and M. Lepovic

Faculty of Electrical Engineering, University of Belgrade, P.O.Box 35–54, 11120 Belgrade, Serbia and Montenegro, ecvetkod@etf.bg.ac.yu
Faculty of Sciences, University of Kragujevac, R. Domanovica 12, 34000 Kragujevac, Serbia and Montenegro lepovic@knez.uis.kg.ac.yu

Abstract: In this paper we study the phenomenon of cospectrality in generalized line graphs and in exceptional graphs. The paper contains a table of sets of cospectral graphs with least eigenvalue at least $-2$ and at most 8 vertices together with some comments and theoretical explanations of the phenomena suggested by the table. In particular, we prove that the multiplicity of the number $0$ in the spectrum of a generalized line graph $L(G)$ is at least the number of petals of the corresponding root graph $G$.

Keywords: graphs; eigenvalues; least eigenvalue; cospectral graphs

Classification (MSC2000): 05C50

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Electronic fulltext finalized on: 6 Oct 2003. This page was last modified: 20 Jun 2011.

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