Let G be a graph of order n and let S be any subset of the vertex set V(G). Denote by GS the graph obtained from the graph G by adding a new vertex x which is adjacent exactly to the vertices from S.

The Annals of Applied Probability, Vol. 20, No. 6 (December 2010), pp. 2086-2117 (32 pages) In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random ...