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Encyclopedia > Topological graph theory

In mathematics topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... A diagram of a graph with 6 vertices and 7 edges. ... In mathematics, a surface is a two-dimensional manifold. ...


Embedding a graph in a surface means we want to draw the graph on a surface, a sphere for example, without two edges intersecting. A basic embedding problem often presented as a mathematical puzzle is the three cottage problem. More important applications can be found in printing electronic circuits where the aim is to print (embed) a circuit (the graph) on a circuit board (the surface) without two connections crossing each other and resulting in a short circuit. A sphere is a perfectly symmetrical geometrical object. ... This article just presents the basic definitions. ... Mathematical games include many topics which are a part of recreational mathematics, but can also cover topics such as the mathematics of games, and playing games with mathematics. ... The three cottage problem is a problem in mathematical graph theory: Suppose there are three cottages that each need to be connected to the gas, water, and electric companies. ... An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... Close-up photo of one side of a motherboard PCB, showing conductive traces, vias and solder points for through-hole components on the opposite side. ... For alternate meanings see Short circuit (disambiguation) A short circuit (sometimes known as simply a short) is a fault whereby electricity moves through a circuit in an unintended path, usually due to a connection forming where none was expected. ...


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  Results from FactBites:
 
PlanetMath: graph theory (506 words)
Graph theory is the branch of mathematics that concerns itself with graphs.
The only remainder of the topological past is the topological graph theory, a branch of graph theory that primarily deals with drawing of graphs on surfaces.
Now, a (finite) graph is usually thought of as a subset of pairs of elements of a finite set (called vertices), or more generally as a family of arbitrary sets in the case of hypergraphs.
PlanetMath: planar graph (540 words)
A planar graph is a graph which can be drawn on a plane (a flat 2-d surface) or on a sphere, with no edges crossing.
Every graph drawn on a sphere can be drawn on a plane (puncture the sphere in the interior of any one of the countries) and vice versa.
planar graphs and embeddings by archibal on 2004-03-30 23:54:21
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