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On the nullspace of arc-transitive graphs over finite fields |
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| Authors: | Primo? Poto?nik Pablo Spiga Gabriel Verret |
| Affiliation: | 1. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia 3. Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia 2. Dipartimento di Matematica ed Applicazioni, University of Milano-Bicocca, Via Cozzi 53, 20125, Milano, Italy |
| Abstract: | Let A be the adjacency matrix of a graph???. 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 ??. 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. |
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