THe largest eigenvalue of sparse random graphs
Michael Krivelevich, Benny Sudakov
Abstract
We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n,p) satisfies almost surely: λ1(G)=(1+o(1))maxΔ,np, where Δis a maximal degree of G, and the o(1) term tends to zero as maxΔ,np tends to infinity.
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