The Balaban 10-cage is one of the three -cage graphs (Read and Wilson
1998, p. 272). The Balaban -cage was the first known example of a 10-cage (Balaban
1973, Pisanski et al. 2001). Embeddings of all three possible -cages (the others being the Harries
graph and Harries-Wong graph) are given
by Pisanski et al. (2001). Several embeddings are illustrated above (e.g.,
Pisanski and Randić 2000).
It is a Hamiltonian graph and has Hamiltonian cycles. It has 1003 distinct LCF
notations, with four of length two (illustrated above) and 999 of length 1.
Balaban, A. T. "Trivalent Graphs of Girth Nine and Eleven and Relationships Among the Cages." Rev. Roumaine Math.18,
1033-1043, 1973.Pisanski, T.; Boben, M.; Marušič, D.; and
Orbanić, A. "The Generalized Balaban Configurations." Preprint. 2001.
http://citeseer.ist.psu.edu/448980.html.Pisanski,
T. and Randić, M. "Bridges between Geometry and Graph Theory." In
Geometry
at Work: A Collection of Papers Showing Applications of Geometry (Ed. C. A. Gorini).
Washington, DC: Math. Assoc. Amer., pp. 174-194, 2000.Read, R. C.
and Wilson, R. J. An
Atlas of Graphs. Oxford, England: Oxford University Press, 1998.Royle,
G. "Cubic Cages." http://school.maths.uwa.edu.au/~gordon/remote/cages/.Wong,
P. K. "Cages--A Survey." J. Graph Th.6, 1-22, 1982.
-cage graphs (Read and Wilson
1998, p. 272). The Balaban 
-cage was the first known example of a 10-cage (Balaban
1973, Pisanski et al. 2001). Embeddings of all three possible 
-cages (the others being the Harries
graph and Harries-Wong graph) are given
by Pisanski et al. (2001). Several embeddings are illustrated above (e.g.,
Pisanski and Randić 2000).
Hamiltonian cycles. It has 1003 distinct LCF
notations, with four of length two (illustrated above) and 999 of length 1.
