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Cubic nonhamiltonian graphs are nonhamiltonian graphs that are also cubic. The numbers of connected cubic nonhamiltonian graphs on n=10, 12, ... nodes are 2, 5, 35, 219, ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

The dihedral group D_3 is a particular instance of one of the two distinct abstract groups of group order 6. Unlike the cyclic group C_6 (which is Abelian), D_3 is ...

An edge-transitive graph is a graph such that any two edges are equivalent under some element of its automorphism group. More precisely, a graph is edge-transitive if for all ...

The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

The Fano plane is the configuration consisting of the two-dimensional finite projective plane over GF(2) ("of order two"), illustrated above. It is a block design with nu=7, ...

The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an ...

For a connected bipartite graph G, the halved graph G^+ and G^- are the two connected components of the distance 2-graph of G. The following table summarizes some named ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

An isosceles tetrahedron is a nonregular tetrahedron in which each pair of opposite polyhedron edges are equal, i.e., a^'=a, b^'=b, and c^'=c, so that all triangular faces ...