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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 405, Pages 138–163 (Mi znsl5284)  
This article is cited in 2 scientific papers (total in 2 papers)

Upper bounds for the second largest eigenvalue of symmetric nonnegative matrices

L. Yu. Kolotilina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (295 kB) Citations (2)
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Abstract: The paper suggests upper bounds on the second largest eigenvalue and the sum of two largest eigenvalues of symmetric nonnegative matrices and graphs. Conditions necessary and sufficient for some of the bounds to be attained are established. Special attention is paid to the subclass of matrices with zero diagonal entries and with off-diagonal entries not exceeding unity, which obviously contains the adjacency matrices of undirected graphs.
Key words and phrases: upper bound for the second largest eigenvalue, Perron root, symmetric nonnegative matrix, sum of eigenvalues, graph eigenvalues.
Received: 15.10.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 191, Issue 1, Pages 75–88
DOI: https://doi.org/10.1007/s10958-013-1305-x
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: L. Yu. Kolotilina, “Upper bounds for the second largest eigenvalue of symmetric nonnegative matrices”, Computational methods and algorithms. Part XXV, Zap. Nauchn. Sem. POMI, 405, POMI, St. Petersburg, 2012, 138–163; J. Math. Sci. (N. Y.), 191:1 (2013), 75–88
Citation in format AMSBIB
\Bibitem{Kol12}
\by L.~Yu.~Kolotilina
\paper Upper bounds for the second largest eigenvalue of symmetric nonnegative matrices
\inbook Computational methods and algorithms. Part~XXV
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 405
\pages 138--163
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5284}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029618}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 191
\issue 1
\pages 75--88
\crossref{https://doi.org/10.1007/s10958-013-1305-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884981068}
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  • https://www.mathnet.ru/eng/znsl/v405/p138
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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