21 research outputs found
On the extreme eigenvalues of regular graphs
In this paper, we present an elementary proof of a theorem of Serre
concerning the greatest eigenvalues of -regular graphs. We also prove an
analogue of Serre's theorem regarding the least eigenvalues of -regular
graphs: given , there exist a positive constant
and a nonnegative integer such that for any -regular graph
with no odd cycles of length less than , the number of eigenvalues
of such that is at least . This
implies a result of Winnie Li.Comment: accepted to J.Combin.Theory, Series B. added 5 new references, some
comments on the constant c in Section