Geodesic
On the nullspace of arc-transitive graphs over finite fields
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 389-401.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let A be the adjacency matrix of a graph $\Gamma $. The nullity of A (that is, the dimension of the nullspace of A), when viewed as a matrix over a field of prime characteristic p, is called the p-nullity of $\Gamma $. We present several families of arc-transitive graphs with arbitrarily large p-nullity. We also show that the p-nullity of a vertex-transitive graph of order a power of p is zero, provided that the valency of the graph is coprime to p.
Keywords: arc-transitive graphs, graph-restrictive groups, spectral graph theory, finite fields 
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     title = {On the nullspace of arc-transitive graphs over finite fields},
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Potočnik, Primož; Spiga, Pablo; Verret, Gabriel. On the nullspace of arc-transitive graphs over finite fields. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 389-401. http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a5/