Search graph database
Browse collections
-
Homeomorphically irreducible trees
Last updated: 15 Dec 2020 | Contains: 1273774 graphs
These are trees with no vertices of degree 2. They are also called series-reduced trees. The following collection was calculated by Brendan McKay (source) and lists all homeomorphically irreducible trees on up to 28 vertices.
-
Tetravalent graphs
Last updated: 15 Dec 2020 | Contains: 906331 graphs
Tetravalent, quartic or 4-regular graphs are graphs where every vertex has degree 4. The following collection was calculated by The House of Graphs (source) and lists all connected tetravalent graphs on up to 15 vertices.
-
Uniquely hamiltonian graphs
Last updated: 15 Dec 2020 | Contains: 142181 graphs
A uniquely hamiltonian graph is a graph which contains exactly one hamiltonian cycle. The following collection was calculated by The House of Graphs (source) and lists all uniquely hamiltonian graphs on up to 10 vertices.
-
Minimal Cayley graphs
Last updated: 22 Dec 2021 | Contains: 3155 graphs
A Cayley graph is a graph that encodes the abstract structure of a group. An undirected graph G is a minimal Cayley graph if there is a group Γ with an inclusion-minimal inverse-closed generating set C such that the Cayley graph Cay(Γ,C) is isomorphic to G. The following collection was calculated...
-
Perihamiltonian graphs
Last updated: 22 Dec 2021 | Contains: 1805 graphs
A graph is perihamiltonian if it is non-hamiltonian but all its edge-contracted subgraphs are hamiltonian. The following collection was calculated by the House of Graphs (source) and lists all perihamiltonian graphs on up to 12 vertices.