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Ball and Coxeter (1987, pp. 277-278) define the ladder graph nP_2, here called the ladder rung graph, of order n as the graph union of n copies of the path graph P_2. The ...

Also called the ménage problem. In how many ways can n married couples be seated around a circular table in such a manner than there is always one man between two women and ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...

Knuth (2008, p. 44) terms the 24-vertex graph based on the notes of the musical scale illustrated above the "musical graph." This graph can be seen to be the 24-vertex case ...

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...

The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

The Perkel graph is a weakly regular graph on 57 vertices and 171 edges, shown above in several embeddings. It is the unique distance-regular graph with intersection array ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

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 ...