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A diagonal matrix D=diag(d_1,...,d_n) sometimes also called the valency matrix corresponding to a graph that has the vertex degree of d_i in the ith position (Skiena 1990, p. ...

A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 ...

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...

The term rectification is sometimes used to refer to the determination of the length of a curve. Rectification also refers to the operation which converts the midpoints of ...

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

Let K subset= C be compact, let f be analytic on a neighborhood of K, and let P subset= C^*\K contain at least one point from each connected component of C^*\K. Then for any ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. ...

The Laplacian spectral ratio R_L(G) of a connected graph G is defined as the ratio of its Laplacian spectral radius to its algebraic connectivity. If a connected graph of ...