Double-star snark
In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges.[1]
Double-star snark | |
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![]() 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 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 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.[3] It has book thickness 3 and queue number 2.[4]
Gallery
- The chromatic number of the double-star snark is 3.
- The chromatic index of the double-star snark is 4.
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References
- Weisstein, Eric W. "Double Star Snark". MathWorld.
- Isaacs, R. (1975), "Infinite families of non-trivial trivalent graphs which are not Tait-colorable", American Mathematical Monthly, Mathematical Association of America, 82 (3): 221–239, doi:10.2307/2319844, JSTOR 2319844
- Weisstein, Eric W. "Hypohamiltonian Graph". MathWorld.
- Wolz, Jessica; Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018
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