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Two functions f(x) and g(x) are orthogonal over the interval a<=x<=b with weighting function w(x) if <f(x)|g(x)>=int_a^bf(x)g(x)w(x)dx=0. (1) If, in addition, ...

A pair of functions phi_i(x) and phi_j(x) are orthonormal if they are orthogonal and each normalized so that int_a^b[phi_i(x)]^2w(x)dx = 1 (1) int_a^b[phi_j(x)]^2w(x)dx = 1. ...

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...

A set A of integers is said to be one-one reducible to a set B (A<<_1B) if there is a one-one recursive function f such that for every x, x in A=>f(x) in B (1) and f(x) in ...

The coarseness xi(G) of a graph G is the maximum number of edge-disjoint nonplanar subgraphs contained in a given graph G. The coarseness of a planar graph G is therefore ...

If the Gauss map of a complete minimal surface omits a neighborhood of the sphere, then the surface is a plane. This was proven by Osserman (1959). Xavier (1981) subsequently ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

The pentatope graph is the skeleton of the pentatope, namely the complete graph K_5. It is sometimes also known as the Kuratowski graph (Nikolić et al. 2000, p. 281). Since ...

The Petersen family of graphs, not to be confused with generalized Petersen graphs, are a set of seven graphs obtained from the Petersen graph (or complete graph K_6) by del ...

Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...