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On the sum of two largest eigenvalues of a symmetric matrixEbrahimi, Javad ...D. Gernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any simple graph is at most the number of vertices of the graph. This can be proved, in particular, for all ... regular graphs. Gernert's conjecture was recently disproved by one of the authors [V. Nikiforov, Linear combinations of graph eigenvalues, Electron. J. Linear Algebra 15 (2006) 329-336], who also provided a nontrivial upper bound for the sum of two largest eigenvalues. In this paper we improve the lower and upper bounds to near-optimal ones, and extend results from graphs to general non-negative matrices.Vir: Special Issue devoted to selected papers presented at the first IPM Conference on Algebraic Graph Theory (Str. 2781-2787)Vrsta gradiva - prispevek na konferenciLeto - 2008Jezik - angleškiCOBISS.SI-ID - 14960473
Avtor
Ebrahimi, Javad |
Mohar, Bojan, 1956- |
Nikiforov, Vladimir |
Sheikh Ahmady, Azhvan
Teme
matematika |
teorija grafov |
matrika sosednosti |
največja lastna vrednost |
spektralni radij |
vsota lastnih vrednosti |
simetrična matrika |
mathematics |
graph theory |
largest eigenvalue |
spectral radius |
eigenvalue sum |
symmetric matrix |
adjacency matrix |
extremal matrix theory
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Ebrahimi, Javad | ![]() |
Mohar, Bojan, 1956- | 01931 |
Nikiforov, Vladimir | ![]() |
Sheikh Ahmady, Azhvan | ![]() |
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