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 , an 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.
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