Ad
related to: euler theorem for planar graphs practice questions worksheet grade 1 computer storage devices- Packets
Perfect for independent work!
Browse our fun activity packs.
- Resources on Sale
The materials you need at the best
prices. Shop limited time offers.
- Assessment
Creative ways to see what students
know & help them with new concepts.
- Free Resources
Download printables for any topic
at no cost to you. See what's free!
- Packets
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.
The first complete proof of this latter claim was published posthumously in 1873 by Carl Hierholzer. [1] This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an even number of incident edges. The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian ...
The Euler characteristic can be defined for connected plane graphs by the same + formula as for polyhedral surfaces, where F is the number of faces in the graph, including the exterior face. The Euler characteristic of any plane connected graph G is 2.
A rotation represented by an Euler axis and angle. In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two ...
Euler also made contributions to the understanding of planar graphs. He introduced a formula governing the relationship between the number of edges, vertices, and faces of a convex polyhedron. Given such a polyhedron, the alternating sum of vertices, edges and faces equals a constant: V − E + F = 2.
For any cycle c in a graph G on m edges, one can form an m-dimensional 0-1 vector that has a 1 in the coordinate positions corresponding to edges in c and a 0 in the remaining coordinate positions. The cycle space C ( G ) of the graph is the vector space formed by all possible linear combinations of vectors formed in this way.
Perfect graph theorem (graph theory) Perlis theorem (graph theory) Planar separator theorem (graph theory) Pólya enumeration theorem (combinatorics) Ramsey's theorem (graph theory, combinatorics) Ringel–Youngs theorem (graph theory) Robbins' theorem (graph theory) Robertson–Seymour theorem (graph theory) Schnyder's theorem (graph theory)
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 ...
Ad
related to: euler theorem for planar graphs practice questions worksheet grade 1 computer storage devices