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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.
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 a graph that can be drawn without crossings in the Euclidean plane.If the points belonging to vertices and edges are removed from the plane, the connected components of the remaining points form polygons, called faces, including an unbounded face extending to infinity.
The triazines have planar six-membered benzene-like ring but with three carbons replaced by nitrogens.The three isomers of triazine are distinguished by the positions of their nitrogen atoms, and are referred to as 1,2,3-triazine, 1,2,4-triazine, and 1,3,5-triazine.
By Steinitz's theorem, a planar graph represents the edges and vertices of a convex polyhedron if and only if it is polyhedral. A three-dimensional polyhedron has a cubic graph if and only if it is a simple polyhedron. And, a planar graph is bipartite if and only if, in a planar embedding of the graph, all face cycles have even length.
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]
A 1-planar graph is said to be an optimal 1-planar graph if it has exactly 4n − 8 edges, the maximum possible. In a 1-planar embedding of an optimal 1-planar graph, the uncrossed edges necessarily form a quadrangulation (a polyhedral graph in which every face is a quadrilateral). Every quadrangulation gives rise to an optimal 1-planar graph ...
In chemistry, pyramidal inversion (also umbrella inversion) is a fluxional process in compounds with a pyramidal molecule, such as ammonia (NH 3) "turns inside out". [1] [2] It is a rapid oscillation of the atom and substituents, the molecule or ion passing through a planar transition state. [3]