CentralNotice Eulerian path From Wikipedia, the free encyclopedia Jump to: navigation , search The Königsberg Bridges graph. This graph is not Eulerian, therefore, a solution does not exist. Every vertex of this graph has an even degree , therefore this is an Eulerian graph. Following the edges in alphabetical order gives an Eulerian circuit/cycle. In graph theory , a Eulerian trail (or Eulerian path ) is a trail in a graph which visits every edge exactly once. Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail which starts and ends on the same vertex . They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. Mathematically the problem can be stated like this: Given the graph in the image, is it possible to construct a path (or a cycle , i.e. a path starting and ending on the same v...