Basically, I want to prove that, in the Kneser graph (wikipedia has a good definition),$K_{n, m}$, if $n_{-}(A(G)) $ and $n_{+}(A(G))$ denote the number of negative and positive eigenvalues of A(G) respectively, then we have

$$\max ({n_{-}A(K_{n, m}), n_{+}(A(K_{n, m}) }) = \binom{n}{m-1}$$

The proof is meant to be in the book "C. Godsil, G. Royle, Algebraic Graph Theory, Springer, 2001." which I do have but can't find, or in the paper http://www.sciencedirect.com/science/article/pii/S0095895602000412 but they only state it as a fact and reference to "] K.N. Vander Meulen, Covers and decompositions of graphs by complete multipartite subgraphs, Ph.D. Thesis, Queen’s University, Kingston, 1995." which I can't seem to get hold of.

If anybody could direct me to the proof, or show me how it is done, I would be immensely grateful.

Many thanks!

Rodger