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Cographs
A cograph, or complement-reducible graph, is a graph that can be generated from the single-vertex 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.
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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.
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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.
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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.
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Edge-transitive graphs
An edge-transitive 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 edge-transitive graphs on up to 47 vertices.