The asymptotic behaviour of Fiedler's algebraic connectivity for random graphs (Q1182983)

In his earlier papers the author dealt with relations between matrices and graphs. Especially, he studied spectra of random graphs [Algebraic methods in graph theory, Vol. I, Conf. Szeged 1978, Colloq. Math. Soc. Janos Bolyai 25, 313-316 (1981; Zbl 0475.05060)]. The algebraic connectivity of a graph \(G\) was introduced by \textit{M. Fiedler} [Czechosl. Math. J. 23(98), 298-305 (1973; Zbl 0265.05119)] as the second smallest eigenvalue of the Laplacian of \(G\). In the paper under review it is shown that if \(G(n)\) is a 2-block random graph with the expectation \(p_{12}\leq p_{11},p_{22}\) then the algebraic connectivity of \(G(n)\) is \(p_{12}n+o(n^{{1\over 2}+\varepsilon})\) in probability.