The spectrum of the edge corona of two graphs

Given two graphs G₁, with vertices 1, 2,., n and edges e₁, e₂,..., e_m, and G₂, the edge corona G₁ {lozenge, open} G₂ of G₁ and G₂ is defined as the graph obtained by taking m copies of G₂ and for each edge e_k = ij of G, joining edges between the two end-vertices i, j of e_k and each vertex of the k-copy of G₂. In this paper, the adjacency spectrum and Laplacian spectrum of G₁ G₂ are given in terms of the spectrum and Laplacian spectrum of G₁ and G₂, respectively. As an application of these results, the number of spanning trees of the edge corona is also considered.