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The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

The cornoid is the curve illustrated above given by the parametric equations x = acost(1-2sin^2t) (1) y = asint(1+2cos^2t), (2) where a>0. It is a sextic algebraic curve with ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. Let such a pentagon have edge lengths a_1, ..., a_5, and area ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

The polar curve r=1+2cos(2theta) (1) that can be used for angle trisection. It was devised by Ceva in 1699, who termed it the cycloidum anomalarum (Loomis 1968, p. 29). It ...

The inner and outer spheres tangent internally to a cone and also to a plane intersecting the cone are called Dandelin spheres. The spheres can be used to show that the ...

A delta sequence is a sequence of strongly peaked functions for which lim_(n->infty)int_(-infty)^inftydelta_n(x)f(x)dx=f(0) (1) so that in the limit as n->infty, the ...