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 proof of minimality of the number of vertices was given by Mary R. O'Keefe and Pak Ken Wong. There are 2 other distinct -cages, the Harries graph and the HarriesâÂÂWong graph. The HarriesâÂÂWong graph and Harries graph are also cospectral.
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
Molecular graph<br/> Balaban 11-cage