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Hypohamiltonian snarks
Last updated: 15 Dec 2020 | Contains: 42285 graphs
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 edge-coloured using 3 colours). Snark is hypohamiltonian if it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex...
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Perfect graphs
Last updated: 15 Dec 2020 | Contains: 146748 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...
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2-arc-transitive tetravalent graphs
Last updated: 20 Dec 2018 | Contains: 165 graphs
This collection contains a list of connected 2-arc-transitive tetravalent graphs on up to 2000 vertices. The list is complete on up to 727 vertices but misses some 7-arc-transitive graphs that admit no s-arc-transitive group for s less than 7 on more than 727 vertices, and also some...
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Self-complementary graphs
Last updated: 15 Dec 2020 | Contains: 710130 graphs
A self-complementary graph is one isomorphic to its complement. Such graphs can only have orders congruent to 0 or 1 modulo 4. Every self-complementary graph is connected and has a diameter of 2 or 3. The following collection was calculated by Brendan McKay (source) and lists all...
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Eulerian graphs
Last updated: 15 Dec 2020 | Contains: 1181670 graphs
The following collection lists all connected graphs with every degree even up to 11 vertices. It was calculated by Brendan McKay (source).