| Double-star snark | |
|---|---|
The Double-star snark |
|
| Vertices | 30 |
| Edges | 45 |
| Chromatic number | 3 |
| Chromatic index | 4 |
| Properties | Snark Hypohamiltonian |
In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges.[1]
In 1975, Rufus Isaacs introduced two infinite families of snarks—the flower snark and the BDS snark, a family that includes the two Blanuša snarks, the Descartes snark and the Szekeres snark (BDS stands for Blanuša Descartes Szekeres).[2] Isaacs also discovered one 30-vertex snark that does not belongs to the BSD family and that is not a flower snark — the double-star snark.
As a snark, the double-star graph is a connected, bridgeless cubic graph with chromatic index equal to 4. The double-star snark is non-planar and non-hamiltonian but is hypohamiltonian.[3]