Balaban 11-cage
Introduction 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.
Gallery 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.
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