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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 419, Pages 139–153 (Mi znsl5742)  

This article is cited in 2 scientific papers (total in 2 papers)

Bounds for the largest two eigenvalues of the signless Laplacian

L. Yu. Kolotilina

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
Full-text PDF (243 kB) Citations (2)
References:
Abstract: In the paper, a new upper bound for the largest eigenvalue $q_1$ of the signless Laplacian $Q_G=D_G+A_G$ of a graph $G$, generalizing and improving the known bound $q_1\le\Delta_1+\Delta_2$, where $\Delta_1\ge\cdots\ge\Delta_n$ are the ordered vertex degrees, and new lower bounds for the second largest eigenvalue $q_2$ of $Q_G$ are proved. As implications, an upper bound for the difference $q_1-\mu_1$ of the largest eigenvalues of the signless Laplacian $Q_G$ and of the Laplacian $L_G=D_G-A_G$, an upper bound for the largest eigenvalue of the adjacency matrix $A_G$, and an upper bound for the difference $q_1-q_2$ are obtained. All the bounds suggested are expressed in terms of the vertex degrees.
Key words and phrases: graph, adjacency matrix, Laplacian, signless Laplacian, largest eigenvalue, second largest eigenvalue, upper bound, lower bound.
Received: 01.11.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 199, Issue 4, Pages 448–455
DOI: https://doi.org/10.1007/s10958-014-1872-5
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: L. Yu. Kolotilina, “Bounds for the largest two eigenvalues of the signless Laplacian”, Computational methods and algorithms. Part XXVI, Zap. Nauchn. Sem. POMI, 419, POMI, St. Petersburg, 2013, 139–153; J. Math. Sci. (N. Y.), 199:4 (2014), 448–455
Citation in format AMSBIB
\Bibitem{Kol13}
\by L.~Yu.~Kolotilina
\paper Bounds for the largest two eigenvalues of the signless Laplacian
\inbook Computational methods and algorithms. Part~XXVI
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 419
\pages 139--153
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5742}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 4
\pages 448--455
\crossref{https://doi.org/10.1007/s10958-014-1872-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902319225}
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  • https://www.mathnet.ru/eng/znsl5742
  • https://www.mathnet.ru/eng/znsl/v419/p139
  • 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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    References:49
     
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