On the extreme eigenvalues of regular graphs
نویسنده
چکیده
In this paper, we present an elementary proof of a theorem of Serre concerning the greatest eigenvalues of k-regular graphs. We also prove an analogue of Serre’s theorem regarding the least eigenvalues of k-regular graphs: given > 0, there exist a positive constant c = c( , k) and a nonnegative integer g = g( , k) such that for any k-regular graph X with no odd cycles of length less than g, the number of eigenvalues μ of X such that μ ≤ −(2 − ) √ k − 1 is at least c|X|. This implies a result of Winnie Li.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 96 شماره
صفحات -
تاریخ انتشار 2006