Balaban 11-cage | |
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The Balaban 11-cage |
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Named after | A. T. Balaban |
Vertices | 112 |
Edges | 168 |
Radius | 6 |
Diameter | 8 |
Girth | 11 |
Automorphisms | 64 |
Chromatic number | 3 |
Chromatic index | 3 |
Properties | Cubic Cage Hamiltonian |
In the mathematical field of graph theory, the Balaban 11-cage or Balaban (3-11)-cage is a 3-regular graph with 112 vertices and 168 edges named after A. T. Balaban.[1]
The Balaban 11-cage is the unique (3-11)-cage. It was discovered by Balaban in 1973.[2] The unicity was proved by McKay and Myrvold in 2003.[3]
The Balaban 11-cage is a Hamiltonian graph and can be constructed by excision from the Tutte 12-cage by removing a small subtree and suppressing the resulting vertices of degree two.[4]
It has chromatic number 3, chromatic index 3, radius 6, diameter 8 and girth 11. It is also a 3-vertex-connected graph and a 3-edge-connected graph.
The characteristic polynomial of the Balaban 11-cage is : .
The automorphism group of the Balaban 11-cage is of order 64.[4]