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The Royle graphs are the two unique simple graphs on eight nodes whose sigma polynomials have nonreal roots (Read and Wilson 1998, p. 265). The sigma polynomials of these ...

The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...

An impossible figure in which a stairway in the shape of a square appears to circulate indefinitely while still possessing normal steps (Penrose and Penrose 1958). The Dutch ...

"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. ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

One of the Zermelo-Fraenkel axioms which asserts the existence for any set a of a set x such that, for any y of a, if there exists a z satisfying A(y,z), then such z exists ...

One of the Zermelo-Fraenkel axioms which asserts the existence of the empty set emptyset. The axiom may be stated symbolically as exists x forall y(!y in x).

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a of the sum (union) x of all sets that are elements of a. The axiom may be stated ...

The bull graph is a simple graph on 5 nodes and 5 edges whose name derives from its resemblance to a schematic illustration of a bull or ram (whose face is the triangle and ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...