Although the real reason does not allow us to see through the nature of the secret nature, thus recognizing the phenomenon, it is still possible this happens: some fictional hypothesis sufficient to explain many phenomena. - Leonhard Euler
origin
Speaking of graph theory, I have to say a big God Euler mathematics, graph theory originated in a very classic problem - Seven Bridges of Königsberg.
In the early 18th century Prussian Konigsberg there is a river, the river there are two small islands. The whole city is divided into four rivers on land, the river is spanned by seven bridges, the four terrestrial links (as shown above). At that time many people are thinking about a question: Can a person walk from a land, not repeated after each bridge once, and finally back to the original point of departure.
Euler was the Seven Bridges of mathematical abstraction. With A, B, C, D represent four land four points, represented by a line between two points is connected to a bridge between two land, is obtained as shown below by a four point seven lines and composition graphics.
In this way, the Seven Bridges is transformed into an abstract graphic whether "one stroke" problem, that is not allowed to leave the pen paper, painted the entire drawing breath; and each line drawn only once promised may not be repeated. Such a pattern can stroke it?
The answer is no.
Because in addition to the start and end points, the rest of the points we called intermediate points. If a stroke of a map may then, for each intermediate point, when the brush reaches this point along a line, along another line must be out of this point, and into this several times, this will leave a few times, into a two by two pair, the wire emanating from this point if the inevitable even number. Thus, whether a one-stroke pattern must meet the following two conditions:
1. 图形必须是连通的。
2. 图中的“奇点”个数是0或2。Note that the "singularity" refers to the number of edges connected to each vertex, i.e., the degree of vertex. Point A of the above figure 5, B, C, D of points are three, four points are connected with the odd edges, in accordance with a stroke that can not be met, thus demonstrating the required Seven Bridges the walk does not exist.
In 1736, 29-year-old Swedish mathematician Euler solved the Seven Bridges of Königsberg. And published the paper "solution with regard to the position of geometric problems," a stroke of the problem are described, was the first use of graph theory and topology model.
Thus the birth of graph theory, graph theory Euler also become the founder of.
Leonhard Euler, Swiss mathematician, natural scientist. Euler was one of the 18th century's most prominent figures in mathematics, he not only several scholars to contribute more to push the whole mathematical physics field.
他是科学史上最多产的一位杰出的数学家，平均每年写出八百多页的论文，还写了大量的力学、分析学、几何学、变分法等的课本，《无穷小分析引论》、《微分学原理》、《积分学原理》等都成为数学界中的经典著作。据统计他那不倦的一生，共写下了886本书籍和论文，其中分析、代数、数论占40%，几何占18%，物理和力学占28%，天文学占11%，弹道学、航海学、建筑学等占3%，彼得堡科学院为了整理他的著作，足足忙碌了四十七年。
一笔画
1. 凡是由偶点组成的连通图，一定可以一笔画成。画时可以把任一偶点为起点，最后一定能以这个点为终点画完此图。
2. 凡是只有两个奇点的连通图（其余都为偶点），一定可以一笔画成。画时必须把一个奇点为起点，另一个奇点为终点。
3. 其他情况的图都不能一笔画出。