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

Gauss's forward formula is f_p=f_0+pdelta_(1/2)+G_2delta_0^2+G_3delta_(1/2)^3+G_4delta_0^4+G_5delta_(1/2)^5+..., (1) for p in [0,1], where delta is the central difference and ...

Newton's forward difference formula is a finite difference identity giving an interpolated value between tabulated points {f_p} in terms of the first value f_0 and the powers ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...

A metric characterizing the difference between two knots K and K^' in S^3.

The inversive distance is the natural logarithm of the ratio of two concentric circles into which the given circles can be inverted. Let c be the distance between the centers ...

The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

The Hamming distance between two vertices of a hypercube is the number of coordinates at which the two vertices differ.