# A result related to the largest eigenvalue of a tree

Gurusamy Rengasamy Vijayakumar

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 3, page 557-561
- ISSN: 2083-5892

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topGurusamy Rengasamy Vijayakumar. "A result related to the largest eigenvalue of a tree." Discussiones Mathematicae Graph Theory 28.3 (2008): 557-561. <http://eudml.org/doc/270599>.

@article{GurusamyRengasamyVijayakumar2008,

abstract = {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.},

author = {Gurusamy Rengasamy Vijayakumar},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {eigenvalues of a graph; characteristic polynomial},

language = {eng},

number = {3},

pages = {557-561},

title = {A result related to the largest eigenvalue of a tree},

url = {http://eudml.org/doc/270599},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Gurusamy Rengasamy Vijayakumar

TI - A result related to the largest eigenvalue of a tree

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 3

SP - 557

EP - 561

AB - 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.

LA - eng

KW - eigenvalues of a graph; characteristic polynomial

UR - http://eudml.org/doc/270599

ER -

## References

top- [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. Zbl0503.05044
- [2] C. Godsil and G. Royle, Algebraic Graph Theory (Springer, New York, 2001). Zbl0968.05002
- [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. Zbl0255.50005
- [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. Zbl0769.05065
- [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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