Regular Two-graphs
The files
as their titles suggest, contain all regular two-graphs on at most
50 vertices that are known to me at this time.
Here each two-graph is identified with
its greatest descendant, where the ordering involved is the natural
one obtained
by expressing as binary integer the
concatenation of the rows
of the upper triangular part of the adjacency matrix. I also list
the order of its automorphism group, and the orbits under the action of
this group. In addition, I include the numbers of strongly regular
graphs that
are obtained either as descendants of the regular two-graph or, where
appropriate, in its switching class. The strongly regular graphs
are identified by their parameters which comprise the number of
vertices and the eigenvalues of their Seidel Spectrum. This
is simply the spectrum of its (-,+) adjacency matrix. The notation
[x,y] means that there are x graphs with automorphism group of order y.
Perhaps the updated files concerning regular two-graphs on 36 and 50
vertices need some explanation. It is now known that there are precisely 227
regular two-graphs
on 36 vertices [1], [2]
and the additional work [3] increased the known number of
regular two-graphs on 50 vertices to 54 (6 self-complementary and
24 complementary pairs).
[1] E. Spence, Regular two-graphs on 36 vertices, Lin. Alg. Appl.
226-228 (1995), 459-497.
[2] Brendan McKay & E Spence, The Classification of Regular Two-graphs on 36 and 38 vertices, Australas. J. Combin.. 24 (2001), 293-300.
[3] E. Spence, Unpublished computer result, 1995