Bridge+of+Königsberg+problem

Bridge Of Konigsberg is the bridge that consist of 7 bridges that connect 4 lands. The problem is to walk through the city without having to cross any bridge more than once. The mathematical graph of the bridge is as below. There are 4 lands labeled as A,B, C, and D. In this graph, all the lands is assume as vertices. There also the bridge that connect each lands which is the edge that connect 2 vertices. Leonhard Euler cannot solve the problems but he came out with some graph theorems, which is Euler circuit and Euler path. Euler path is a path which traverses each edge of the graph exactly once. While Euler Circuit is a path that one can traverse along every edge of the graph once to each of the other vertices and return to vertex.

In this problem, we use euler path to solve it, which says that the degree of the starting vertex and last vertex can be odd, but the degree of rest of the vertices must be even .While, euler circuit can also be use,if someone want to finished their journey at the same land he start his journey.The condition is for euler circuit, the degree of each vertex must be even values. It is represent the path someone go out from the land and get in to the land.

So, this bridge of konigsberg cannot be solve due to the degree of all the vertices is odd. It can be solve only if we add some vertices or edges on the graph to make the vertices follows euler theorems. Below is some of the demonstration of euler path:

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