Concept

# Flower snark

Summary
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 Jn can be constructed with the following process :
• Build n copies of the star graph on 4 vertices. Denote the central vertex of each star Ai and the outer vertices Bi, Ci and Di. This results in a disconnected graph on 4n vertices with 3n edges (Ai – Bi, Ai – Ci and Ai – Di for 1 ≤ i ≤ n).
• Construct the n-cycle (B1... Bn). This adds n edges.
• Finally construct the 2n-cycle (C1... CnD1... Dn). This adds 2n edges.
By construction, the Flower snark Jn is a cubic graph with 4n vertices and 6n edges. For it to have the required properties, n should be odd. Special cases The name fl
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