Graph structure
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Posted On :
Sep-27-2010
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Article Word Count :
480
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In recent years, increasingly growing interest in this field of mathematics as the theory of graphs.
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And the thing is that graph theory is applied in fields such as physics, chemistry, communication theory, design computers, electronics, engineering, architecture, operations research, genetics, psychology, sociology, economics, anthropology and linguistics.
This theory is closely connected with many areas of mathematics, among them - group theory, matrix theory, numerical analysis, probability theory, topology and combinatorial analysis.
Graph Theory is the mathematical model for any system containing a binary relation.
Also, the graphs are attractive and have aesthetic appeal due to their representation in the form of diagrams.
Although many results in graph theory, elementary in nature, it is also a tremendous wealth of very thin combinatorial problems worthy of attention the most sophisticated mathematicians.
Graphs - Opening!
In 1736 in the city of Königsberg (now Kaliningrad, Russia) were the two islands connected by bridges with seven banks of the river Pregolya and with each other. The task consisted of the following: find a route passing all four parts of the land, which would begin with any of them would have ended on the same side and only once through each bridge. It is easy, of course, to try to solve this problem empirically, making search of all routes, but all attempts will fail.
To prove that the problem has no solution, a distinguished mathematician of the XVIII century, an academician of the Petersburg Academy of Sciences - Leonard Euler - marked every piece of sushi point (apex), and each axle - a line (edge) connecting the corresponding points. Received "graph".
Statement about the nonexistence of "positive" solution for this problem is equivalent to saying that it is impossible to bypass a special way the graph presented in Fig.
Starting from this particular case, Euler generalized the problem and found a criterion for the existence of bypass (special path) in a given graph, namely, the graph must be connected and each vertex must be associated with an even number of edges. Graph, shown in the figure, is connected, but each vertex is associated with an even number of edges.
Thus, the graph is a pair (V, E), where V - non-empty set of objects of a certain nature, called the vertices of the graph, and E - a subset of two-element subsets of V, called edges of the graph.
Intelligent Graph Visualizer
This program is designed to work with such an abstract data type as a graph.
A graph is a pair (V, E), where V - non-empty set of objects of a certain nature, called the vertices of the graph, and E - a subset of two-element subsets of V, called edges of the graph.
Based on these characteristics of the graph can be obtained by others.
All basic operations are guaranteed to work for a classical undirected graph with edges without negative weights.
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Article Source :
http://www.articleseen.com/Article_Graph structure_34786.aspx
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Author Resource :
First believe in yourself, then others will believe you.FFXIV Gil
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Keywords :
ffxiv gil,
Category :
Arts and Entertainment
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Arts and Entertainment
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