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Tutte's (46-vertex) graph is a cubic nonhamiltonian graph contructed by Tutte (1946) as a counterexample to Tait's Hamiltonian graph conjecture by using three copies ...

The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...

A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

The Barnette-Bosák-Lederberg graph is a graph on 38 vertices which is the smallest known example of a planar 3-connected nonhamiltonian graph, i.e., the smallest known ...

The truncated icosahedral graph is the cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated icosahedron. It is sometimes known as the ...

A graph G on more than two vertices is said to be k-connected (or k-vertex connected, or k-point connected) if there does not exist a vertex cut of size k-1 whose removal ...

A nonhamiltonian graph is a graph that is not Hamiltonian. All disconnected graphs are therefore nonhamiltoinian, as are acylic graphs. Classes of connected graphs that are ...

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...

A graph cycle.

The snub dodecahedral graph is a quintic graph on 60 nodes and 150 edges that corresponds to the skeleton of the snub dodecahedron, great inverted snub icosidodecahedron, ...