Balaban 10-cage
Introduction In the mathematical field of graph theory, the '''Balaban 10-cage''' or '''Balaban -cage''' is a 3-regular graph with 70 vertices and 105 edges named after Alexandru T. Balaban. Published in 1972, It was the first 10-cage discovered but it is not unique.The complete list of 10-cages and the proof of minimality was given by Mary R. O'Keefe and Pak Ken Wong. There exist 3 distinct -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 3-edge-connected. The book thickness is 3 and the queue number is 2.The characteristic polynomial of the Balaban 10-cage is:  :
Gallery Image:balaban_10-cage_2COL.svg|The chromatic number of the Balaban 10-cage is 2.Image:balaban_10-cage_3color_edge.svg|The chromatic index of the Balaban 10-cage is 3.Image: balaban_10-cage_alternative_drawing.svg|Another drawing of the Balaban 10-cage.
See also Molecular graphBalaban 11-cage
References