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There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

A Halin graph, sometimes known as a roofless polyhedron, is a polyhedral graph constructed from a planar embedding of a tree having four or more vertices, no vertices of ...

Given a commutative ring R, an R-algebra H is a Hopf algebra if it has additional structure given by R-algebra homomorphisms Delta:H->H tensor _RH (1) (comultiplication) and ...

A regularly spaced array of points in a square array, i.e., points with coordinates (m,n,...), where m, n, ... are integers. Such an array is often called a grid or mesh, and ...

Let lim stand for the limit lim_(x->c), lim_(x->c^-), lim_(x->c^+), lim_(x->infty), or lim_(x->-infty), and suppose that lim f(x) and lim g(x) are both zero or are both ...

In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

The smallest value of a set, function, etc. The minimum value of a set of elements A={a_i}_(i=1)^N is denoted minA or min_(i)a_i, and is equal to the first element of a ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

The transformation of a sequence a_1, a_2, ... with a_n=sum_(d|n)b_d (1) into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n=sum_(d|n)mu(n/d)a_d. (2) The ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...