On the nullspace of arc-transitive graphs over finite fields
نویسندگان
چکیده
Let A be the adjacency matrix of a graph Γ . 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 Γ . We present several families of arc-transitive graphs with arbitrarily large p-nullity. We also show that the p-nullity of a vertextransitive graph of order a power of p is zero, provided that the valency of the graph is coprime to p.
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