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The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

The icosahedral graph is the Platonic graph whose nodes have the connectivity of the regular icosahedron, as well as the great dodecahedron, great icosahedron Jessen's ...

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

Machin-like formulas have the form mcot^(-1)u+ncot^(-1)v=1/4kpi, (1) where u, v, and k are positive integers and m and n are nonnegative integers. Some such formulas can be ...

The molecular topological index is a graph index defined by MTI=sum_(i=1)^nE_i, where E_i are the components of the vector E=(A+D)d, with A the adjacency matrix, D the graph ...

The m×n queen graph Q_(m,n) is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a queen. ...

The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

"Casting out nines" is an elementary check of a multiplication which makes use of the congruence 10^n=1 (mod 9). Let decimal numbers be written a=a_n...a_2a_1a_0, ...

Flower graphs are a name given in this work to the generalization of the flower snarks J_n for positive n=5, 7, 9, ... to all integer n>=5. They are illustrated above for n=5 ...