Graph Theory

Graphs. Find in depth. In this paper, a short-I would like to touch on the theme of graphs and pathfinding. For those who do not know a graph – a collection of some objects related to each other. In today's world graphs are used almost everywhere: navigation and geographic information systems, and various engineering services, telecommunication lines and power transmission system (transmission lines, substations, etc.), chemistry … The list goes on almost endlessly. Graph Theory interesting in that it allows us to describe (and solve) the problem is difficult to measurable mathematical description without the use of graphs.

It is worth noting that the graph theory now contains a large number of unsolved problems than attracts more attention. I would like to mention one interesting moment associated with the search in depth in the graph. But first, some theory. Graphs are different. In order to make you understand everything written below, we consider the most general notions of graph theory: weighted graph (weighted graph) – a graph in which each edge (ie the relationship between the vertices), has its own weight. In the unweighted graph all edges have the same weight (respectively, it does not matter what it will be).

A directed graph (directed graph) – a graph in which edges have directions. Ie transition in such a graph from one vertex to another is irreversible (you can not go back on the same edge). Orienirovanny graph similar to unilateral network of roads connecting certain objects (including the fact that on each edge of the traffic cops are in any case, take away the right =).