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A finite, increasing sequence of integers {n_1,...,n_m} such that sum_(i=1)^m1/(n_i)-product_(i=1)^m1/(n_i) in N. A sequence is a Giuga sequence iff it satisfies ...

The Goh-Schmutz constant is defined by the integrals C = int_0^infty(ln(1+t))/(e^t-1)dt (1) = int_0^inftyln[1-ln(1-e^(-t))]dt (2) = ...

The Goldberg graphs are a family of graphs discovered by Goldberg (1981) which are snarks for n=5, 7, 9, .... Precomputed properties of Goldberg graphs are implemented in the ...

The mathematical golden rule states that, for any fraction, both numerator and denominator may be multiplied by the same number without changing the fraction's value.

G = int_0^infty(e^(-u))/(1+u)du (1) = -eEi(-1) (2) = 0.596347362... (3) (OEIS A073003), where Ei(x) is the exponential integral. Stieltjes showed it has the continued ...

An algebraic ring which appears in treatments of duality in algebraic geometry. Let A be a local Artinian ring with m subset A its maximal ideal. Then A is a Gorenstein ring ...

The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...

The cube of a graph is defined as its third graph power.

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).