| Flower snark | |
| Notation: | Jn with n odd |
| Vertices: | 4n |
| Edges: | 6n |
| Girth: | 3 for n=3 5 for n=5 6 for n≥7 |
| Chromatic Number: | 3 |
| Chromatic Index: | 4 |
| Properties: | Snark for n≥5 |
| Book Thickness: | 3 for n=5 3 for n=7 |
| Queue Number: | 2 for n=5 2 for n=7 |
| Flower snark J5 | |
| Vertices: | 20 |
| Edges: | 30 |
| Girth: | 5 |
| Chromatic Number: | 3 |
| Chromatic Index: | 4 |
| Properties: | Snark Hypohamiltonian |
In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975.[1]
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.[2]
The flower snark Jn can be constructed with the following process :
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.
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.[3] In order to avoid trivial cases, snarks are generally restricted to have girth at least 5. With that restriction, J3 is not a snark.