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Elsevier, Discrete Mathematics, 11(313), p. 1162-1166

DOI: 10.1016/j.disc.2011.11.024

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On graphs with an eigenvalue of maximal multiplicity

Journal article published in 2013 by Peter Rowlinson
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

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).