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If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

A plane-filling arrangement of plane figures or its generalization to higher dimensions. Formally, a tiling is a collection of disjoint open sets, the closures of which cover ...

A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...

A curve with polar coordinates, r=b+asectheta (1) studied by the Greek mathematician Nicomedes in about 200 BC, also known as the cochloid. It is the locus of points a fixed ...

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...

Given a planar graph G, a geometric dual graph and combinatorial dual graph can be defined. Whitney showed that these are equivalent (Harary 1994), so that one may speak of ...

The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. ...

If A=>B and B=>A (i.e., A=>B ^ B=>A, where => denotes implies), then A and B are said to be equivalent, a relationship which is written symbolically in this work as A=B. The ...

Consider the recurrence equation defined by a_0=m and a_n=|_sqrt(2a_(n-1)(a_(n-1)+1))_|, (1) where |_x_| is the floor function. Graham and Pollak actually defined a_1=m, but ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...