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Graphs cospectral with Kneser graphs. (English) Zbl 1232.05125
Brualdi, Richard A. (ed.) et al., Combinatorics and graphs. Selected papers based on the presentations at the 20th anniversary conference of IPM on combinatorics, Tehran, Iran, May 15–21, 2009. Dedicated to Reza Khosrovshahi on the occasion of his 70th birthday. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4865-4/pbk). Contemporary Mathematics 531, 159-164 (2010).
Summary: We construct graphs that are cospectral but nonisomorphic with Kneser graphs $$K(n, k)$$, when $$n= 3k- 1$$, $$k> 2$$ and for infinitely many other pairs $$(n, k)$$. We also construct nonisomorphic cospectral graphs for the Modulo-2 Kneser graph $$K_2(n, k)$$ when $$3\leq k\leq n-3$$.
For the entire collection see [Zbl 1202.05003].

##### MSC:
 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05E30 Association schemes, strongly regular graphs
##### Keywords:
nonisomorphic cospectral graphs; Johnson scheme