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The Frucht graph is smallest cubic identity graph (Skiena 1990, p. 185). It is implemented in the Wolfram Language as GraphData["FruchtGraph"]. It has 12 vertices and 18 ...

Frucht's theorem states that every finite group is the automorphism group of a finite undirected graph. This was conjectured by König (1936) and proved by Frucht (1939). In ...

If f^'(x) is continuous and the integral converges, int_0^infty(f(ax)-f(bx))/xdx=[f(0)-f(infty)]ln(b/a).

A frustum (unfortunately commonly misspelled "frustrum") is that portion of a solid which lies between two parallel planes cutting the solid. Degenerate cases are obtained ...

If the average number of envelopes per pigeonhole is a, then some pigeonhole will have at least a envelopes. Similarly, there must be a pigeonhole with at most a envelopes.

Fubini's theorem, sometimes called Tonelli's theorem, establishes a connection between a multiple integral and a repeated one. If f(x,y) is continuous on the rectangular ...

A system of linear differential equations (dy)/(dz)=A(z)y, (1) with A(z) an analytic n×n matrix, for which the matrix A(z) is analytic in C^_\{a_1,...,a_N} and has a pole of ...

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

The Fuhrmann center Fu is the center of the Fuhrmann circle, given by the midpoint of the line joining the Nagel point and orthocenter (which forms a diameter of the Fuhrmann ...