Flower snark
Introduction In the mathematical field of graph theory, the '''flower snarks''' form an infinite family of snarks introduced by Rufus Isaacs in 1975.As snarks, the flower snarks are connected, bridgeless cubic graphs with chromatic index equal to 4.The flower snarks are non-planar and non-hamiltonian. The flower snarks  J5 and J7 have book thickness 3 and queue number 2.
Construction The flower snark J''n'' can be constructed with the following process :* Build ''n'' copies of the star graph on 4 vertices. Denote the central vertex of each star A''i'' and the outer vertices B''i'', C''i'' and D''i''. This results in a disconnected graph on 4''n'' vertices with 3''n'' edges (A''i'' – B''i'', A''i'' – C''i'' and A''i'' – D''i'' for 1 ≤ ''i'' ≤ ''n''). * Construct the ''n''-cycle (B1... B''n''). This adds ''n'' edges. * Finally construct the ''2n''-cycle (C1... C''n''D1... D''n''). This adds ''2n'' edges.By construction, the Flower snark J''n'' is a cubic graph with 4''n'' vertices and 6''n'' edges. For it to have the required properties, ''n'' should be odd.
Special cases The name flower snark is sometimes used for J5, a flower snark with 20 vertices and 30 edges. It is one of 6 snarks on 20 vertices . The flower snark J5 is hypohamiltonian.J3 is a trivial variation of the Petersen graph formed by replacing one of its vertices by a triangle. This graph is also known as the Tietze's graph. In order to avoid trivial cases, snarks are generally restricted to have girth at least 5.With that restriction, J3 is not a snark.
Gallery File:Flower snark 3COL.svg|The chromatic number of the flower snark J5 is 3.File:Flower_snark_4color edge.svg|The chromatic index of the flower snark J5 is 4.File:Flower_snark_original.svg|The original representation of the flower snark J5.File:Flower-Petersen-minor.svg|The Petersen graph as a graph minor of the flower snark J5
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