Discussiones Mathematicae Graph Theory 28(3) (2008) 557-561
doi: 10.7151/dmgt.1427

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A RESULT RELATED TO THE LARGEST EIGENVALUE OF A TREE

Gurusamy Rengasamy Vijayakumar

School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road, Colaba, Mumbai 400 005, India
e-mail: vijay@math.tifr.res.in

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.

Keywords: eigenvalues of a graph, characteristic polynomial.

2000 Mathematics Subject Classification: 05C50, 15A18.

References

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Received 3 October 2007
Revised 10 June 2008
Accepted 10 June 2008