The Balaban 10-cage
|Named after||A. T. Balaban|
In the mathematical field of graph theory, the Balaban 10-cage or Balaban (3,10)-cage is a 3-regular graph with 70 vertices and 105 edges named after A. T. Balaban. Published in 1972, It was the first (3,10)-cage discovered but is not unique.
The complete list of (3-10)-cage and the proof of minimality was given by O'Keefe and Wong. There exists 3 distinct (3-10)-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 characteristic polynomial of the Balaban 10-cage is : .
- Weisstein, Eric W., "Balaban 10-Cage", MathWorld.
- A. T. Balaban, A trivalent graph of girth ten, J. Combin. Theory Ser. B 12, 1-5. 1972.
- Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. "The Generalized Balaban Configurations." Preprint. 2001. .
- M. O'Keefe and P.K. Wong, A smallest graph of girth 10 and valency 3, J. Combin. Theory Ser. B 29 (1980) 91-105.
- Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.