Integral complete multipartite graphs

We give counterexamples to a result in F. Esser and F. Harary [2, Theorem 3] asserting that two nonisomorphic complete r-partite graphs with the same number of vertices have different spectral radii. We then derive some results on invariant factors and apply them to obtain relationship between the parameters of integral complete multipartite graphs and their integer eigenvalues. Necessary conditions for complete multipartite graphs to be integral are obtained.