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Cographs
A cograph, or complementreducible graph, is a graph that can be generated from the singlevertex graph K1 by complementation and disjoint union. The following collection was calculated by Atila A. Jones (source) and lists all connected cographs on up to 15 vertices.

Ramsey(3,4) graphs
A Ramsey(s,t) graph is a graph with no clique of size s, and no independent set of size t. The following collection was calculated by Brendan McKay (source) and lists all Ramsey(3,4) graphs.

Ramsey(3,5) graphs
A Ramsey(s,t) graph is a graph with no clique of size s, and no independent set of size t. The following collection was calculated by Brendan McKay (source) and lists all Ramsey(3,5) graphs.

Ramsey(3,6) graphs
A Ramsey(s,t) graph is a graph with no clique of size s, and no independent set of size t. The following collection was calculated by Brendan McKay (source) and lists all Ramsey(3,6) graphs.

Edgetransitive graphs
An edgetransitive graph is a graph such that any two edges are equivalent under some element of its automorphism group. The following collection was calculated by Lucas Mol (source) and lists all edgetransitive graphs on up to 47 vertices.