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Let a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G. Then G is "generically" rigid in R^2 iff e^'<=2n^'-3 for every subgraph of G having ...

The edge set of a graph is simply a set of all edges of the graph. The cardinality of the edge set for a given graph g is known as the edge count of g. The edge set for a ...

The mean distance of a (connected) graph is the mean of the elements of its graph distance matrix. Closed forms for some classes of named graphs are given in the following ...

The number of graph edges meeting at a given node in a graph is called the order of that graph vertex.

A Hilbert space is a vector space H with an inner product <f,g> such that the norm defined by |f|=sqrt(<f,f>) turns H into a complete metric space. If the metric defined by ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

The Coxeter configuration is a 12_3 configuration whose Levi graph is the Nauru graph.

Barban's constant is defined as C_(Barban) = product_(p)[1+(3p^2-1)/(p(p+1)(p^2-1))] (1) = 2.596536... (2) (OEIS A175640), where the product is over the primes p.

The Cartesian product of a finite or infinite set of modules over a ring with only finitely many nonzero entries in each sequence.