Double-star snark
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| Double-star snark | |
|---|---|
 The Double-star snark | |
| Vertices | 30 |
| Edges | 45 |
| Radius | 4 |
| Diameter | 4 |
| Girth | 6 |
| Automorphisms | 80 |
| Chromatic number | 3 |
| Chromatic index | 4 |
| Book thickness | 3 |
| Queue number | 2 |
| Properties | Snark Hypohamiltonian |
| Table of graphs and parameters | |
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 belong to the BDS 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 but is 1-planar.[3] It is non-hamiltonian but is hypohamiltonian.[4] It has book thickness 3 and queue number 2.[5]
