Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs
نویسندگان
چکیده
منابع مشابه
Extreme eigenvalues of nonregular graphs
Let λ1 be the greatest eigenvalue and λn the least eigenvalue of the adjacency matrix of a connected graph G with n vertices, m edges and diameter D. We prove that if G is nonregular, then Δ− λ1 > nΔ− 2m n(D(nΔ− 2m)+ 1) 1 n(D + 1) , where Δ is the maximum degree of G. The inequality improves previous bounds of Stevanović and of Zhang. It also implies that a lower bound on λn obtained by Alon an...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2021
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-021-01054-4