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In graph theory, a branch of mathematics, a periodic graph with respect to an operator F on graphs is one for which there exists an integer n > 0 such that F n (G) is isomorphic to G. [1] For example, every graph is periodic with respect to the complementation operator , whereas only complete graphs are periodic with respect to the operator ...
The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Kepler published the first two laws in 1609 and the third law in 1619. They supplanted earlier models of the Solar System, such as those of Ptolemy and Copernicus .
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
As an example of the application of Noether's theorem is the example of stationary space-times and their associated Komar mass.(Komar 1959). While general space-times lack a finite-parameter time-translation symmetry, stationary space-times have such a symmetry, known as a Killing vector. Noether's theorem proves that such stationary space ...
A metric graph embedded in the plane with three open edges. The dashed line denotes the metric distance between two points and .. A metric graph is a graph consisting of a set of vertices and a set of edges where each edge = (,) has been associated with an interval [,] so that is the coordinate on the interval, the vertex corresponds to = and to = or vice versa.
An aperiodic graph. The cycles in this graph have lengths 5 and 6; therefore, there is no k > 1 that divides all cycle lengths. A strongly connected graph with period three. In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph.
[1] [2] A Euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory, as well as to discrete geometry and the theory of polytopes, and similar areas.
The co-moving wavenumber corresponding to the maximum power in the mass power spectrum is determined by the size of the cosmic particle horizon at the time of matter-radiation equality, and therefore depends on the mean density of matter and to a lesser extent on the number of neutrino families (), = (/) =, for = .