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An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...
A toroidal graph is a graph that can be embedded without crossings on the torus. More generally, the genus of a graph is the minimum genus of a two-dimensional surface into which the graph may be embedded; planar graphs have genus zero and nonplanar toroidal graphs have genus one. Every graph can be embedded without crossings into some ...
An embedded system on a plug-in card with processor, memory, power supply, and external interfaces. An embedded system is a specialized computer system—a combination of a computer processor, computer memory, and input/output peripheral devices—that has a dedicated function within a larger mechanical or electronic system.
An embedded submanifold (also called a regular submanifold), is an immersed submanifold for which the inclusion map is a topological embedding. That is, the submanifold topology on S {\displaystyle S} is the same as the subspace topology.
A coordinate map, a coordinate chart, or simply a chart, of a manifold is an invertible map between a subset of the manifold and a simple space such that both the map and its inverse preserve the desired structure. [2]
The way it is embedded in space; There are examples of networks, which seem to be not "directly" embedded in space. Social networks for instance connect individuals through friendship relations. But in this case, space intervenes in the fact that the connection probability between two individuals usually decreases with the distance between them.
Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) {,} = {} which is not in {{,},}. To allow loops, the definitions must be expanded.