Search Results for ""

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...

A graph vertex in a graph is said to be an odd node if its vertex degree is odd.

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

Any finite semigroup is a divisor for an alternating wreath product of finite groups and semigroups.

A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

A bivector, also called a 2-vector, is an antisymmetric tensor of second rank (a.k.a. 2-form). For a bivector X^->, X^->=X_(ab)omega^a ^ omega^b, where ^ is the wedge product ...

Let f be an integer polynomial. The f can be factored into a product of two polynomials of lower degree with rational coefficients iff it can be factored into a product of ...

The infinite product identity Gamma(1+v)=2^(2v)product_(m=1)^infty[pi^(-1/2)Gamma(1/2+2^(-m)v)], where Gamma(x) is the gamma function.

The Hajós number h(G) of a graph G is the maximum k such that G contains a subdivision of the complete graph K_k.