Balaban 10-cage
| Balaban 10-cage | |
|---|---|
The Balaban 10-cage
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| Named after | A. T. Balaban |
| Vertices | 70 |
| Edges | 105 |
| Radius | 6 |
| Diameter | 6 |
| Girth | 10 |
| Automorphisms | 80 |
| Chromatic number | 2 |
| Chromatic index | 3 |
| Properties |
Cubic Cage Hamiltonian |
In the mathematical field of graph theory, the Balaban 10-cage or Balaban (3,10)-cage is a 3-regular graph with 70 vertices and 105 edges named after A. T. Balaban. Published in 1972, It was the first (3,10)-cage discovered but is not unique.
The complete list of (3-10)-cage and the proof of minimality was given by O'Keefe and Wong. There exists 3 distinct (3-10)-cages, the other two being the Harries graph and the Harries–Wong graph. Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.
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 a 3-edge-connected graph.
The characteristic polynomial of the Balaban 10-cage is
The chromatic number of the Balaban 10-cage is 2.
The chromatic index of the Balaban 10-cage is 3.
Alternative drawing of the Balaban 10-cage.
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