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 vertex-transitive graph of order a power of p is zero, provided that the valency of the graph is coprime to p.
Potočnik, P., Spiga, P., Verret, G. (2012). On the nullspace of arc-transitive graphs over finite fields. JOURNAL OF ALGEBRAIC COMBINATORICS, 36(3), 389-401 [10.1007/s10801-011-0340-2].
On the nullspace of arc-transitive graphs over finite fields
SPIGA, PABLO
;
2012
Abstract
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 vertex-transitive graph of order a power of p is zero, provided that the valency of the graph is coprime to p.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
