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: :(x-3) x^{12} (x^2-6)^5 (x^2-2)^{12} (x^3-x^2-4 x+2)^2\cdot :\cdot(x^3+x^2-6 x-2) (x^4-x^3-6 x^2+4 x+4)^4 \cdot :\cdot(x^5+x^4-8 x^3-6 x^2+12 x+4)^8. The automorphism group of the Balaban 11-cage is of order 64.
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