A short proof of a theorem of Bang and Koolen A. Mohammadian a, b a, 1

Let a graph Γ be locally disjoint union of three copies of complete graphs Kq−1 and let Γ be cospectral with the Hamming graph H(3, q). Bang and Koolen [Asian-Eur. J. Math. 1 (2008), 147–156] proved that if q> 3, then Γ is isomorphic to H(3, q). We present a short proof of this result