घूर्णन-तंत्र इसके अंग्रेजी अर्थ का उदाहरण

Mizan's appointment was the fourth following a second rotation system amongst the nine Malay Rulers.

It consisted of a rotation system of off-loading turns: four teams of off-loading turns made up of both Neapolitans and Sicilians, helped each other smuggle, off-load and distribute the goods.

Lum (disambiguation) In combinatorial mathematics, rotation systems (also called combinatorial embeddings) encode embeddings of graphs onto orientable surfaces, by describing the circular ordering of a graph's edges around each vertex.

A more formal definition of a rotation system involves pairs of permutations; such a pair is sufficient to determine a multigraph, a surface, and a 2-cell embedding of the multigraph onto the surface.

Conversely, any embedding of a connected multigraph G on an oriented closed surface defines a unique rotation system having G as its underlying multigraph.

This fundamental equivalence between rotation systems and 2-cell-embeddings was first settled in a dual form by Lothar Heffter in the 1890s and extensively used by Ringel during the 1950s.

A rotation system specifies a circular ordering of the edges around each vertex, while a rotation map specifies a (non-circular) permutation of the edges at each vertex.

In addition, rotation systems can be defined for any graph, while as Reingold et al.

Formally, a rotation system is defined as a pair (σ,θ) where σ and θ are permutations acting on the same ground set B, θ is a fixed-point-free involution, and the group "lt;σ,θ"gt; generated by σ and θ acts transitively on B.

To derive a rotation system from a 2-cell embedding of a connected multigraph G on an oriented surface, let B consist of the darts (or flags, or half-edges) of G; that is, for each edge of G we form two elements of B, one for each endpoint of the edge.

If a multigraph is embedded on an orientable but not oriented surface, it generally corresponds to two rotation systems, one for each of the two orientations of the surface.

These two rotation systems have the same involution θ, but the permutation σ for one rotation system is the inverse of the corresponding permutation for the other rotation system.

Recovering the embedding from the rotation system .

To recover a multigraph from a rotation system, we form a vertex for each orbit of σ, and an edge for each orbit of θ.