Geodesic
Tight estimates for eigenvalues of regular graphs
The electronic journal of combinatorics, Tome 11 (2004) no. 1

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Zbl EuDML
It is shown that if a $d$-regular graph contains $s$ vertices so that the distance between any pair is at least $4k$, then its adjacency matrix has at least $s$ eigenvalues which are at least $2 \sqrt {d-1} \cos \big({\pi\over 2 k}\big)$. A similar result has been proved by Friedman using more sophisticated tools.
DOI : 10.37236/1850
Classification : 05C50
Mots-clés : adjacency matrix, eigenvalues 
A. Nilli. Tight estimates for eigenvalues of regular graphs. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1850
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     author = {A. Nilli},
     title = {Tight estimates for eigenvalues of regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1850},
     zbl = {1053.05082},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1850/}
}
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