کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603283 1631166 2008 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the sum of two largest eigenvalues of a symmetric matrix
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the sum of two largest eigenvalues of a symmetric matrix
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issues 11–12, 1 December 2008, Pages 2781-2787