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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 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
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
A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches.
Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period. For a function on the real numbers or on the integers , that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals.
The Laves graph. In geometry and crystallography, the Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three equal-length segments meet at 120° angles at each point, and all cycles use ten or more segments.
This category is for graphs defined in terms of relations for or structures of geometric objects. ... Penny graph; Periodic graph (geometry) Permutation graph; Planar ...
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