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Trigonal planar: Molecules with the trigonal planar shape are somewhat triangular and in one plane (flat). Consequently, the bond angles are set at 120°. For example, boron trifluoride. Angular: Angular molecules (also called bent or V-shaped) have a non-linear shape. For example, water (H 2 O), which has an angle of about 105°. A water ...
A planar graph is said to be convex if all of its faces (including the outer face) are convex polygons. Not all planar graphs have a convex embedding (e.g. the complete bipartite graph K 2,4). A sufficient condition that a graph can be drawn convexly is that it is a subdivision of a 3-vertex-connected planar graph.
For undirected planar graphs, one way to construct an arc diagram with at most two semicircles per edge is to subdivide the graph and add extra edges so that the resulting graph has a Hamiltonian cycle (and so that each edge is subdivided at most once), and to use the ordering of the vertices on the Hamiltonian cycle as the ordering along the ...
In contrast, the extra stability of the 7p 1/2 electrons in tennessine are predicted to make TsF 3 trigonal planar, unlike the T-shaped geometry observed for IF 3 and predicted for AtF 3; [39] similarly, OgF 4 should have a tetrahedral geometry, while XeF 4 has a square planar geometry and RnF 4 is predicted to have the same. [40]
In liquid crystals homogeneous alignment, sometimes called planar alignment, is the state of alignment where molecules align in parallel to a substrate. The opposite method is homeotropic alignment .
For planar digraphs, a much faster method is available, as described by Mikkel Thorup in 2004. [6] This method can answer reachability queries on a planar graph in () time after spending () preprocessing time to create a data structure of () size. This algorithm can also supply approximate shortest path distances, as well as route ...
An affidavit previously obtained by the local news stations stated that Jacob left his girlfriend's house, saying he was going to have dinner with his family.
A 1-planar drawing of the Heawood graph: six of the edges have a single crossing, and the remaining 15 edges are not crossed.. In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point, where it crosses a single additional edge.