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"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...

Attach a string to a point on a curve. Extend the string so that it is tangent to the curve at the point of attachment. Then wind the string up, keeping it always taut. The ...

An irreducible representation of a group is a group representation that has no nontrivial invariant subspaces. For example, the orthogonal group O(n) has an irreducible ...

The Laplacian for a scalar function phi is a scalar differential operator defined by (1) where the h_i are the scale factors of the coordinate system (Weinberg 1972, p. 109; ...

The Laplacian matrix, sometimes also called the admittance matrix (Cvetković et al. 1998, Babić et al. 2002) or Kirchhoff matrix, of a graph G, where G=(V,E) is an ...

If f(z) is analytic throughout the annular region between and on the concentric circles K_1 and K_2 centered at z=a and of radii r_1 and r_2<r_1 respectively, then there ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions. To examine the behavior of an orbit around a point ...

Marion's theorem (Mathematics Teacher 1993, Maushard 1994, Morgan 1994) states that the area of the central hexagonal region determined by trisection of each side of a ...