Balaban 10-cage
Template:Short description Template:Infobox graph
In the mathematical field of graph theory, the Balaban 10-cage or Balaban Template:Math-cage is a 3-regular graph with 70 vertices and 105 edges named after Alexandru T. Balaban.[1] Published in 1972,[2] It was the first 10-cage discovered but it is not unique.[3]
The proof of minimality of the number of vertices was given by Mary R. O'Keefe and Pak Ken Wong.[4] There are 2 other distinct Template:Math-cages, the Harries graph and the Harries–Wong graph.[5] The Harries–Wong graph and Harries graph are also cospectral.
The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 6, girth 10 and is hamiltonian. It is also a 3-vertex-connected graph and 3-edge-connected. The book thickness is 3 and the queue number is 2.[6]
The characteristic polynomial of the Balaban 10-cage is
Gallery
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The chromatic number of the Balaban 10-cage is 2. -
The chromatic index of the Balaban 10-cage is 3. -
Another drawing of the Balaban 10-cage.
See also
Molecular graph
Balaban 11-cage
References
- ↑ Template:MathWorld
- ↑ Alexandru T. Balaban, A trivalent graph of girth ten, Journal of Combinatorial Theory Series B 12 (1972), 1–5.
- ↑ Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. The Generalized Balaban Configurations. Preprint. 2001.
- ↑ Mary R. O'Keefe and Pak Ken Wong, A smallest graph of girth 10 and valency 3, Journal of Combinatorial Theory Series B 29 (1980), 91–105.
- ↑ Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.
- ↑ Jessica Wolz, Engineering Linear Layouts with SAT. Master Thesis, Universität Tübingen, 2018