Search results
Results from the WOW.Com Content Network
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 ...
On a planar graph, both axes represent the mole fractions of the lighter (lower boiling) component; the horizontal (x) and vertical (y) axes represents the liquid and vapor phase compositions, respectively. The x = y line (see Figure 1) represents the scenarios where the compositions of liquid and vapor are the same.
Graph drawing also can be said to encompass problems that deal with the crossing number and its various generalizations. The crossing number of a graph is the minimum number of intersections between edges that a drawing of the graph in the plane must contain. For a planar graph, the crossing number is zero by definition. Drawings on surfaces ...
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. ...
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 ...
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]