extends the previous alpha-adjacency matrix. This matrix is designated the (a, b)-adjacency matrix of g. Both adjacency matrices are examples of universal matrices already studied by W. Haemers. In this paper, we study the (a, b)-adjacency spectra for a family of compound graphs formed by disjoint balanced trees whose roots are identified to the vertices of a given graph. In consequence, new families of cospectral (adjacency, Laplacian and signless Laplacian) graphs, new hypoenergetic graphs (graphs whose energy is less than its vertex number) and new explicit formulae for Estrada, signless Laplacian Estrada and Laplacian Estrada indices of graphs were obtained. Moreover, sharp upper bounds of the above indices for caterpillars, in terms of length of the path and of the maximum number of its pendant vertices, are given. (C) 2017 Elsevier Inc. All rights reserved.