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 J_k, of order 4k and a Goldberg snark, say B_k, of order 8k. We determine the automorphic groups of J_k and B_k for every k and prove that they are isomorphic to the dihedral group D_4k of order 4k.
Infinite classes of dihedral snarks / Fiori, Carla; Ruini, Beatrice. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - STAMPA. - 5:2(2008), pp. 199-210. [10.1007/s00009-008-0144-3]
Infinite classes of dihedral snarks
FIORI, Carla;RUINI, Beatrice
2008
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 J_k, of order 4k and a Goldberg snark, say B_k, of order 8k. We determine the automorphic groups of J_k and B_k for every k and prove that they are isomorphic to the dihedral group D_4k of order 4k.
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