Elsevier, Discrete Mathematics, 11(313), p. 1162-1166
DOI: 10.1016/j.disc.2011.11.024
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Let G be a graph of order n with an eigenvalue μ≠-1,0 of multiplicity k2. The only known examples with k=½t(t-1) are 3K2 (with n=6, μ=1, k=3) and the maximal exceptional graph G36 (with n=36, μ=-2, k=28). We show that no other example can be constructed from a strongly regular graph in the same way as G36 is constructed from the line graph L(K9).