planarity

The first level of Planarity is built with lines, so it has vertices and edges.

No wonder the smooth planarity of city life appealed to two of the Six.

Its large size and planarity have also shown promise as a chromatographic separation material.

The smaller the value of n the larger the deviation from aromatic planarity.

In one such system deformation from planarity is found similar to that of tetrahelicene.

The best pieces possess a strong lyricism and planarity.

The planarity of the peptide bonds can be imposed as a further constraint.

Planarity of the molecule has proven to be essential for maximum potency.

Such complexes are further subdivided according to the planarity or pyramidalization at sulfur.

The complete statement on the planarity of graphs (the Planar graph) encompasses this result.

Efficient planarity testing is fundamental to graph drawing.

It is evident that subdividing a graph preserves planarity.

It is closely related to planarity in that the more planar the molecule the stronger its aromaticity.

Other reports suggest that the aromaticity (and planarity) can vary between arsole derivatives.

The source code for the planarity test and the extraction of multiple Kuratowski subdivisions is publicly available.

The use of Ramachandran angles comes about from the well known planarity of the peptide bond.

See for an experimental comparison with a preliminary version of the Boyer and Myrvold planarity test.

A similar method has been followed by Schnyder to prove enhanced bounds and a characterization of planarity based on the incidence partial order.

The para-substituted phenol ring is bent about 15 out of planarity, adopting a somewhat boat-like geometry.

A number of results on upward planarity and on crossing-free Hasse diagram construction are known:

Further, the bonding has less restrictions, concerning substrate roughness and planarity than direct bonding.

DFS is the basis for many graph-related algorithms, including topological sorts and planarity testing.

In this compound the deviation from planarity is 13 for the benzene ring and 17 for the bridgehead carbons.

The sp-sp carbon carbon bonds are out of planarity with the benzene rings by 20 .

While graph drawing can be a difficult problem, force-directed algorithms, being physical simulations, usually require no special knowledge about graph theory such as planarity.