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A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

Ahmed's integral is the definite integral int_0^1(tan^(-1)(sqrt(x^2+2)))/(sqrt(x^2+2)(x^2+1))dx=5/(96)pi^2 (OEIS A096615; Ahmed 2002; Borwein et al. 2004, pp. 17-20). This is ...

A regular pyramid is a right pyramid whose base is a regular polygon. For a right pyramid of height h with a regular n-gonal base of side length a and circumradius R, the ...

The Gray graph is a cubic semisymmetric graph on 54 vertices. It was discovered by Marion C. Gray in 1932, and was first published by Bouwer (1968). Malnič et al. (2002) ...

An ideal is a subset I of elements in a ring R that forms an additive group and has the property that, whenever x belongs to R and y belongs to I, then xy and yx belong to I. ...

The Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

Let F(n,sigma) denote the number of permutations on the symmetric group S_n which avoid sigma in S_k as a subpattern, where "tau contains sigma as a subpattern" is ...

The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...

The tetrakis hexahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

The truncated octahedron is the 14-faced Archimedean solid with faces 8{6}+6{4}. It is also the uniform polyhedron with Maeder index 8 (Maeder 1997), Wenninger index 7 ...