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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.
In chemistry, trigonal planar is a molecular geometry model with one atom at the center and three atoms at the corners of an equilateral triangle, called peripheral atoms, all in one plane. [1] In an ideal trigonal planar species, all three ligands are identical and all bond angles are 120°. Such species belong to the point group D 3h.
For example, sulfur hexafluoride (SF 6) is an octahedral molecule. Trigonal pyramidal : A trigonal pyramidal molecule has a pyramid-like shape with a triangular base. Unlike the linear and trigonal planar shapes but similar to the tetrahedral orientation, pyramidal shapes require three dimensions in order to fully separate the electrons.
As a non-Hamiltonian maximal planar graph, the Goldner–Harary graph provides an example of a planar graph with book thickness greater than two. [5] Based on the existence of such examples, Bernhart and Kainen conjectured that the book thickness of planar graphs could be made arbitrarily large, but it was subsequently shown that all planar ...
K 1 through K 4 are all planar graphs. However, every planar drawing of a complete graph with five or more vertices must contain a crossing, and the nonplanar complete graph K 5 plays a key role in the characterizations of planar graphs: by Kuratowski's theorem, a graph is planar if and only if it contains neither K 5 nor the complete bipartite ...
Pages in category "Planar graphs" The following 88 pages are in this category, out of 88 total. This list may not reflect recent changes. ...
Structure of cisplatin, an example of a molecule with the square planar coordination geometry. In chemistry, the square planar molecular geometry describes the stereochemistry (spatial arrangement of atoms) that is adopted by certain chemical compounds. As the name suggests, molecules of this geometry have their atoms positioned at the corners.
A chemical graph is a labeled graph whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. Its vertices are labeled with the kinds of the corresponding atoms and edges are labeled with the types of bonds. [1] For particular purposes any of the labelings may be ignored. A hydrogen-depleted molecular graph ...