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The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...

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 ...

The generalization of the Schönflies theorem to n dimensions. A smoothly embedded n-hypersphere in an (n+1)-hypersphere separates the (n+1)-hypersphere into two components, ...

The polynomials M_k(x;delta,eta) which form the Sheffer sequence for g(t) = {[1+deltaf(t)]^2+[f(t)]^2}^(eta/2) (1) f(t) = tan(t/(1+deltat)) (2) which have generating function ...

The metabidiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(81). The unit metabidiminished rhombicosidodecahedron has volume ...

The Moser spindle is the 7-node unit-distance graph illustrated above (Read and Wilson 1998, p. 187). It is sometimes called the Hajós graph (e.g., Bondy and Murty 2008. p. ...

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 18-sided polygon, sometimes also called an octakaidecagon.

There are a number of attractive polyhedron compounds consisting of ten octahedra. These compounds will be implemented in a future version of the Wolfram Language as ...

There are a number of attractive polyhedron compounds consisting of 12 octahedra. This compound will be implemented in a future version of the Wolfram Language as ...