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Citation

Bell FK & Rowlinson P (2003) On the multiplicities of graph eigenvalues. Bulletin of the London Mathematical Society, 35 (3), pp. 401-408. https://doi.org/10.1112/S0024609303002030

Abstract
Star complements and associated quadratic functions are used to obtain a sharp upper bound for the order of a graph with an eigenspace of prescribed codimension. It is shown that for regular graphs the bound can be reduced by 1, and that this reduced bound is attained by a regular graph G if and only if G is an extremal strongly regular graph. 2000 Mathematics Subject Classification 05C50.

Journal
Bulletin of the London Mathematical Society: Volume 35, Issue 3