Infinite Classes of Dihedral Snarks

Abstract.Flower snarks and Goldberg snarks are two infinite families of cyclically 5–edge–connected cubic graphs with girth at least five and chromatic index four. For any odd integer k, k > 3, there is a Flower snark, say Jk, of order 4k and a Goldberg snark, say Bk, of order 8k. We determine the automorphism groups of Jk and Bk for every k and prove that they are isomorphic to the dihedral group D4k of order 4k.