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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 ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...

A sequence of real numbers {x_n} is equidistributed on an interval [a,b] if the probability of finding x_n in any subinterval is proportional to the subinterval length. The ...

A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive are noncayley graphs. However, some vertex-transitive graph are noncayley. ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

Euclid's second theorem states that the number of primes is infinite. The proof of this can be accomplished using the numbers E_n = 1+product_(i=1)^(n)p_i (1) = 1+p_n#, (2) ...

The Gegenbauer polynomials C_n^((lambda))(x) are solutions to the Gegenbauer differential equation for integer n. They are generalizations of the associated Legendre ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...