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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....

Edgetransitive tetravalent graphs
The collection provides information about connected edgetransitive graphs of degree 4. This second edition shows graphs of up to 150 vertices. It is known to be incomplete in a few ways. We hope, eventually, to expand the range up to 512 vertices (to include Bouwer's generalization of the Gray...

Vertextransitive graphs
This page lists all the transitive graphs on up to 31 vertices. The data was prepared by Brendan McKay and Gordon Royle (source). The current extension has been made possible by the work of Alexander Hulpke who has constructed all the transitive groups of degree up to 31.
At this stage the numbers...

Hexagonal capping of symmetric cubic graphs
Hexagonal capping HC(G) has four vertices {u0, v0},{u0, v1},{u1, v0},{u1, v1} for each edge {u,v} of G, and each {u_i, v_j} is joined to each {v_j, w_(1i)}, where u and w are distinct neighbors of v in G. The collection includes hexagonal capping of cubic symmetric graphs up to 798 vertices.

Line graphs of symmetric cubic graphs
Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint ("are incident") in G. The collection includes line graphs of cubic symmetric graphs with...