Some infinite classes of asymmetric nearly Hamiltonian snarks

  • Carla Fiori
  • Beatrice Ruini
Keywords: Full automorphism group, Snark, Nearly hamiltonian snark


We determine the full automorphism group of each member of three infinite families of connected cubic graphs which are snarks. A graph is said to be nearly hamiltonian if it has a cycle which contains all vertices but one. We prove, in particular, that for every possible order n ≥ 28 there exists a nearly hamiltonian snark of order n with trivial automorphism group.