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Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

Let A^' be the outermost vertex of the regular pentagon erected inwards on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

A lattice graph, also known as a mesh graph or grid graph, is a graph possessing an embedding in a Euclidean space R^n that forms a regular tiling. Examples include grid ...

A linear algebraic group is a matrix group that is also an affine variety. In particular, its elements satisfy polynomial equations. The group operations are required to be ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

Let A^' be the outermost vertex of the regular pentagon erected outward on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

The pentagonal wegde is one of the seven topologically distinct convex hexahedra. Like the cube, it contains 8 vertices, 12 edges, and 6 faces, but its faces consist of 2 ...

The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of n sides is r/R=(cot(pi/n))/(csc(pi/n))=cos(pi/n). (1) ...

The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...