A snark is a nontrivial cubic graph with chromatic index 4.

The FlowerSnark command creates the flower snark graphs, also known as Isaac's snarks. A flower snark with parameter K, is a 3-regular graph on 4*K vertices. The GoldbergSnark(K) command creates the Goldberg snark with parameter K. A Goldberg snark with parameter K, is a 3-regular graph on 8*K vertices.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$F≔\mathrm{FlowerSnark}\left(5\right)$

$F≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 20\; vertices\; and\; 30\; edge(s)}$

$\mathrm{IsRegular}\left(F\right)$

$\mathrm{true}$

$\mathrm{DrawGraph}\left(F\right)$

$\mathrm{ChromaticIndex}\left(F\right)$

$4$

$\mathrm{CircularChromaticNumber}\left(F\right)$

$\frac{5}{2}$

$H≔\mathrm{GoldbergSnark}\left(5\right)$

$H≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 40\; vertices\; and\; 60\; edge(s)}$

$\mathrm{DrawGraph}\left(H\right)$