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Concept
Balaban 11-cage
Summary
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 Alexandru T. Balaban.
The Balaban 11-cage is the unique (3,11)-cage. It was discovered by Balaban in 1973. The uniqueness was proved by Brendan McKay and Wendy Myrvold in 2003.
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.
It has independence number 52, 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.
Image:balaban_11-cage_3COL.svg|The [[chromatic number]] of the Balaban 11-cage is 3.
Image:balaban_11-cage_3color_edge.svg|The [[chromatic index]] of the Balaban 11-cage is 3.
Image: balaban_11-cage_alternative_drawing.svg|Alternative drawing of the Balaban 11-cage.[[Peter Eades|P. Eades]], J. Marks, [[Petra Mutzel|P. Mutzel]], S. North. "Graph-Drawing Contest Report", TR98-16, December 1998, Mitsubishi Electric Research Laboratories.
Official source
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