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Eulerian Graph

Can we travel along the edges of a graph starting at a vertex and returning to it by traversing each edge of the graph exactly once?

This question an easily be answered simply by examining the degrees of the vertices of the graph.

Figure 1: The Seven Bridges of Konigsberg Figure 2: Multigraph Model of

the Town of Konigsberg

  • An Euler path is a path using every edge of graph G exactly once.
  • An Euler circuit is a circuit using every edge of the graph G exactly once.
  • An Euler path starts and ends at different vertices.
  • An Euler circuit starts and ends at the same vertex.

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