Monday, May 25, 2009

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forum # 2 Graphs: software tool for learning and solving real problems.

Graphs: A software tool for building, editing and analysis that can be useful for teaching, learning and problem solving also for related disciplines such as operations research, network design, industrial engineering, logistics and transportation among others. A graph can be represented as a network model a business reality. This model can be analyzed from different points of view because the algorithms and functions built into the tool. In computer science, can be used without restrictions.
graphs are the natural representation of the networks, which are each again included.
are mathematical artifacts that allow visually express a very simple and effective relationships that exist between elements of various kinds. A simple graph consists of two sets:
• A set V of points called vertices or nodes.
• A set of pairs of vertices called edges or arcs that indicate which nodes are related.
In a more informal way we can say that a graph is a set of nodes with links between them, called edges or arcs.
Example:
A graph consists of a set of nodes (or vertices) and a set of arcs. Each arc in a graph is specified by a pair of nodes.
The set of nodes is {A, B, C, D, F, G, H} and the set of arcs {(A, B), (A, D), (A, C), (C, D) (C, F), (E, G), (A, A)} for the following graph

TERMINOLOGY
*.- The number of nodes in the graph is called the order of the graph.
*.- A null graph is a graph of order 0 (zero). *.-
Two nodes are adjacent if there is an arc that joins them.
*.- In a directed graph, if A is adjacent to B, B is not necessarily adjacent
*.- A Path is a sequence of one or more arcs that connect two nodes.
*.- A graph is called connected when there is always a path linking any two nodes
and disconnected otherwise.
*.- A graph is complete when each node is connected with every one of the remaining nodes.
*.- The path of a node and it is called a cycle.
The philosophy of this tool is the following: drawing, model, solve and analyze. " This is intended that the user has absolute freedom to discuss and address problems. You can draw freely without worrying graph analysis or algorithm to be used later. The program will warn you if it is impracticable or any other requirement for a particular analysis. The graphs using a learning experience based on their freedom and-error testing stages (Learning through play).
Example: Graph Implementation in means of transport.



Video:
http://www.youtube.com/watch?v=iMJXWYz9vE0

According to the concept graph, apply a daily life example.

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