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 J k , of order 4k and a Goldberg snark, say B k , of order 8k. We determine the automorphism 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. Mathematics Subject Classification (2000). Primary 05C25; Secondary 20B25.

Odd 2-factored snarks

“…Fix the labelling on the vertices of J(t) as defined in Section 2. The flower snark has the dihedral group D 2t as automorphism group [13], its edge-orbits are four and its vertex-orbits are three.…”

“…Recall that the flower snark has the dihedral group D 2t as automorphism group ( [13]) with vertex orbits [h 1 ] := {h i : i = 1, . .…”

Computing the Automorphic Chromatic Index of Certain Snarks

“…Proof. The automorphism group Aut(J k ) of J k (see [1]) is isomorphic to the dihedral group D 4k of order 4k, with generators τ :…”

“…The determination of the full automorphism groups of graphs in a given infinite family is in general no easy task. Presentations for the automorphism groups of Flower snarks and Goldberg snarks have already been determined in [1]. We are aware of no such presentation for Blanuša snarks.…”