Distance between the spectra of graphs with respect to normalized Laplacian spectra

Let G(n) and G(n)' be two nonisomorphic graphs on n vertices with spectra (with respect to the adjacency matrix) lambda(1) >= lambda(2) >= . . . >=lambda n and lambda(1)' >= lambda(2)'lambda >= . . . >= lambda(n)' respectively. Define the distance between the spectra of G(n) and G(n)', as lambda(G(n), G(n)') = Sigma(n)(i=1)(lambda(i)-lambda(i)')(2) (or use Sigma(n)(i=1) vertical bar lambda(i)-lambda(i)'vertical bar). Define the cospectrality of G(n) by cs(G(n)) = min {lambda(G(n), G(n)') : G'(n) not isomorphic to G(n)}. In this paper, we investigate cs(G(n)) for special classes of graphs with respect to normalized Laplacian spectra and we find cs(K-n), cs(nK(1)) and cs(K-2 + (n - 2)K-1) (n >= 2). We also find an upper bound for cs(n).