All connected cubic vertex-transitive graphs of order at most $1280$.

Id of the graph in the dataset. A graph is uniquely identified by the id and the order.

The number of vertices in the largest clique subgraph.

The greatest distance between any pair of vertices.

Length of the shortest cycle in the graph.

For every two ordered pairs of adjacent vertices, does there exist an authomorphism, mapping one to the other.

Can the vertices of the graph be partitioned into two sets, such that every edge connects a vertex in one set to a vertex in the other set.

Can the graph be constructed as a Cayley graph of some group for some generating set.

For any two vertices $v$ and $w$, the number of vertices at distance $j$ from $v$ and at distance $k$ from $w$ depends only upon $j$, $k$, and $i = d(v, w)$.

Given any two vertices $v$ and $w$ at any distance $i$, and any other two vertices $x$ and $y$ at the same distance, there is an automorphism of the graph that carries $v$ to $x$ and $w$ to $y$.

For every two edges, does there exist an authomorphism, mapping one to the other.

Does the graph have a cycle that visits each vertex exactly once.

Is the graph isometric to a subgraph of a hypercube.

Can the vertices of the graph be partitioned into a clique and an independent set.

Do there exists $\lambda$ and $\mu$ such that every two adjacent vertices have $\lambda$ common neighbours and every two non-adjacent vertices have $\mu$ common neighbours.

The number of cycles of length $3$ in the graph.

Does the graph belong to the Split Praeger-Xu family of graphs.

A census of small connected cubic vertex-transitive graphs

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