Author’s abstract: Given two graphs \(G_1\) with vertices \(\{v_1,v_2,\dots,v_n\}\) and \(G_2\), the neighbourhood corona, \(G_1\star G_2\) is the graph obtained by taking \(n\) copies of \(G_2\) and for each \(i\), making all vertices in the \(i\)-th copy of \(G_2\) adjacent with the neighbours of \(v_i\), \(i=1,2,\dots,n\). A complete description of the spectrum and eigenvectors of \(G_1\star G_2\) is given when \(G_2\) is regular.