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Hypohamiltonian snarks
A snark is a connected bridgeless cubic graph (i.e., a biconnected cubic graph) with edge chromatic number of four (i.e. it cannot be properly edgecoloured using 3 colours). Snark is hypohamiltonian if it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex...

Perfect graphs
A perfect graph is a simple graph such that for every induced subgraph, its clique number equals its chromatic number. A graph is also perfect if and only if neither the graph nor its complement graph has a chordless cycle of odd order, where a chord is an edge that is not part of the cycle but...

2arctransitive tetravalent graphs
This collection contains a list of connected 2arctransitive tetravalent graphs on up to 2000 vertices. The list is complete on up to 727 vertices but misses some 7arctransitive graphs that admit no sarctransitive group for s less than 7 on more than 727 vertices, and also some...

Selfcomplementary graphs
A selfcomplementary graph is one isomorphic to its complement. Such graphs can only have orders congruent to 0 or 1 modulo 4. Every selfcomplementary graph is connected and has a diameter of 2 or 3. The following collection was calculated by Brendan McKay (source) and lists all...

Eulerian graphs
The following collection lists all connected graphs with every degree even up to 11 vertices. It was calculated by Brendan McKay (source).