Vertices 30 Radius 4 Girth 6 | Edges 45 Diameter 4 Automorphisms 80 | |
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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.
References
Double-star snark Wikipedia(Text) CC BY-SA