Symmetric cubic graphs (The Foster Census)
Trivalent (cubic) connected symmetric graphs on up to 2048 vertices.
Ronald M. Foster started collecting specimens of small cubic symmetric graphs prior to 1934, maintaining a census of all such graphs. In 1988 the then current version of the census was published by I.Z. Bouwer, W.W. Chernoff, B. Monson and Z. Star in a book entitled The Foster Census (Charles Babbage Research Centre, 1988), which contained data for the graphs on up to 512 vertices.
The list of known cubic symmetric graphs with less than 1000 vertices was collated in 2001 by Gordon Royle, Marston Conder, Brendan McKay and Peter Dobscanyi (source).
Cubic symmetric graphs up to 2048 vertices were found by Marston Conder (University of Auckland) with the help of the
LowIndexNormalSubgroups routine in Magma, in August 2006 (source).