Double-star snark

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
Properties	Snark Hypohamiltonian

In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges.

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). Isaacs also discovered one 30-vertex snark that does not belongs 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 and non-hamiltonian but is hypohamiltonian.

The chromatic number of the double-star snark is 3.

The chromatic index of the double-star snark is 4.