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An identity graph, sometimes also known as an asymmetric graph or rigid graph (Albertson and Collins 1996), is a graph possessing a single graph automorphism. The numbers of ...

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

The Randić matrix A_(Randic) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=1/(sqrt(d_id_j)), (1) where d_i are the vertex degrees of the graph. In ...

The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p)=0 for primes p. The first few ...

Let sum_(k=0)^(infty)a_k=a and sum_(k=0)^(infty)c_k=c be convergent series such that lim_(k->infty)(a_k)/(c_k)=lambda!=0. Then ...

The genus gamma(G) of a graph G is the minimum number of handles that must be added to the plane to embed the graph without any crossings. A graph with genus 0 is embeddable ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...

|_n]!={n! for n>=0; ((-1)^(-n-1))/((-n-1)!) for n<0. (1) The Roman factorial arises in the definition of the harmonic logarithm and Roman coefficient. It obeys the identities ...

An n-mark Golomb ruler is a set of n distinct nonnegative integers (a_1,a_2,...,a_n), called "marks," such that the positive differences |a_i-a_j|, computed over all possible ...

The cross polytope beta_n is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (+/-1, 0, 0, ..., 0). A ...