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A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations induce symmetries of that graph (i.e., application of any such translation to the graph embedded in the Euclidean space leaves the graph unchanged). Equivalently, a periodic Euclidean graph is ...
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 ...
Periodic points of f(z) = z*z−0.75 for period =6 as intersections of 2 implicit curves. The degree of the equation () = is 2 n; thus for example, to find the points on a 3-cycle we would need to solve an equation of degree 8. After factoring out the factors giving the two fixed points, we would have a sixth degree equation.
The global unpolarized period domain is the quotient of the local unpolarized period domain by the action of Γ (it is thus a collection of double cosets). In the polarized case, the elements of the monodromy group are required to also preserve the bilinear form Q , and the global polarized period domain is constructed as a quotient by Γ in ...
In crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes are points in three-dimensional Euclidean space, and whose edges (or bonds or spacers) are line segments connecting pairs of vertices, periodic in three linearly independent axial directions.
Periodic graph may refer to: Periodic graph (crystallography) or crystal net, a Euclidean graph representing the atomic or molecular structure of a crystal; Periodic graph (geometry), a Euclidean graph preserved under a lattice of translations; Periodic graph (graph theory), a graph that is periodic with respect to a graph theoretic operator
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