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## Discussiones Mathematicae Graph Theory

2008 | 28 | 3 | 557-561
Tytuł artykułu

### A result related to the largest eigenvalue of a tree

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Języki publikacji
EN
Abstrakty
EN
In this note we prove that {0,1,√2,√3,2} is the set of all real numbers l such that the following holds: every tree having an eigenvalue which is larger than l has a subtree whose largest eigenvalue is l.
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
557-561
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-10-03
poprawiono
2008-06-10
zaakceptowano
2008-06-10
Twórcy
• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India
Bibliografia
• [1] M. Doob, A surprising property of the least eigenvalue of a graph, Linear Algebra and Its Applications 46 (1982) 1-7, doi: 10.1016/0024-3795(82)90021-0.
• [2] C. Godsil and G. Royle, Algebraic Graph Theory (Springer, New York, 2001).
• [3] P.W.H. Lemmens and J.J. Seidel, Equiangular lines, Journal of Algebra 24 (1973) 494-512, doi: 10.1016/0021-8693(73)90123-3.
• [4] L. Lovász, Combinatorial Problems and Exercises (North-Holland Publishing Company, Amsterdam, 1979).
• [5] A.J. Schwenk, Computing the characteristic polynomial of a graph, in: Graphs and Combinatorics, eds. R.A. Bari and F. Harary, Springer-Verlag, Lecture Notes in Math. 406 (1974) 153-172.
• [6] N.M. Singhi and G.R. Vijayakumar, Signed graphs with least eigenvalue < -2, European J. Combin. 13 (1992) 219-220, doi: 10.1016/0195-6698(92)90027-W.
• [7] J.H. Smith, Some properties of the spectrum of a graph, in: Combinatorial Structures and their Applications, eds. R. Guy, H. Hanani, N. Sauer and J. Schönheim, Gordon and Breach, New York (1970), 403-406.
• [8] D.B. West, Introduction to Graph Theory, Second edition (Printice Hall, New Jersey, USA, 2001).
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Bibliografia
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