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A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...

A quintic nonhamiltonian graph is a quintic graph that is nonhamiltonian. A number of such graphs are illustrated above. Owens (1980) showed that there exists a ...

"The" tetrahedral graph is the Platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph K_4 and therefore also the wheel graph W_4. ...

A number of attractive tetrahedron 10-compounds can be constructed. The first (left figures) can be obtained by combining tetrahedron 5-compounds of opposite chirality ...

The Thomson problem is to determine the stable equilibrium positions of n classical electrons constrained to move on the surface of a sphere and repelling each other by an ...

The 12-vertex graph consisting of a cube in which two opposite faces (say, top and bottom) have edges drawn across them which connect the centers of opposite sides of the ...

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform ...

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...