Small cutsets in arc-transitive digraphs of prime degree

We give an upper bound for the size of non-trivial sets that have small boundary in a family of arc-transitive digraphs. We state the exact size for these sets in case of prime degree. We also give a lower bound for the size of a minimum non-trivial cutset in the case of arc-transitive Cayley digraphs of prime degree.Research supported by the Spanish Research Council under project MTM2011-28800-C02-01 and by the Catalan Research Council under grant 2009SGR1387