Elusive groups of automorphisms of digraphs of small valency
  A transitive permutation group is called elusive if it contains no semiregular element. We show that no group of automorphisms of a connected graph of valency at most four is elusive and determine all the elusive groups of automorphisms of connected digraphs of out-valency at most three. 
Michael Giudici, Luke Morgan, Primo\v{z} Poto\v{c}nik, Gabriel Verret
math.CO math.GR