Search Results for ""

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

The (upper) clique number of a graph G, denoted omega(G), is the number of vertices in a maximum clique of G. Equivalently, it is the size of a largest clique or maximal ...

The "contiguous USA graph" is the graph whose vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect ...

The modified bessel function of the second kind is the function K_n(x) which is one of the solutions to the modified Bessel differential equation. The modified Bessel ...

A quadratic form Q(z) is said to be positive definite if Q(z)>0 for z!=0. A real quadratic form in n variables is positive definite iff its canonical form is ...

The absolute square of a complex number z, also known as the squared norm, is defined as |z|^2=zz^_, (1) where z^_ denotes the complex conjugate of z and |z| is the complex ...

The modulus of a complex number z, also called the complex norm, is denoted |z| and defined by |x+iy|=sqrt(x^2+y^2). (1) If z is expressed as a complex exponential (i.e., a ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...

In elliptic cylindrical coordinates, the scale factors are h_u=h_v=sqrt(sinh^2u+sin^2v), h_z=1, and the separation functions are f_1(u)=f_2(v)=f_3(z)=1, giving a Stäckel ...