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A simplex, sometimes called a hypertetrahedron (Buekenhout and Parker 1998), is the generalization of a tetrahedral region of space to n dimensions. The boundary of a ...

The singleton graph is the graph consisting of a single isolated node with no edges. It is therefore the empty graph on one node. It is commonly denoted K_1 (i.e., the ...

A stacked (or generalized) prism graph Y_(m,n) is a simple graph given by the graph Cartesian product Y_(m,n)=C_m square P_n (Gallian 2007) for positive integers m,n with ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...

The biconnected graph theta_0 on seven nodes and seven edges illustrated above. It has chromatic polynomial pi_(theta_0)(z)=z^7-8z^6+28z^5-56z^4+68z^3-47z^2+14z and chromatic ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

Trigonometric functions of npi/7 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 7 is not a ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

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 regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...