Math 2.0

definition

Eulerian trail

Definition

Let GG be a graph or a multigraph. An Eulerian trail of GG is a trail in GG that uses every edge of GG exactly once. An Eulerian circuit is an Eulerian trail that starts and ends at the same vertex.

Remarks

A graph with an Eulerian circuit is called Eulerian. Euler's theorem characterizes the connected graphs with an Eulerian circuit by the parity of the degrees. The Seven Bridges of Königsberg form a multigraph with no Eulerian trail.

Explanations

L1 human

An Eulerian trail draws the whole graph in one stroke, without lifting the pen and without going over any line twice. An Eulerian circuit also ends where it starts.

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Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionTrail, definition, no evidence levelTraildefinitionEulerian trail, definition, no evidence levelEulerian traildefinition
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  1. Graph definition
  2. Walk definition
  3. Trail definition
  4. Eulerian trail definition

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Sources

  1. Web https://en.wikipedia.org/wiki/Eulerian_path, Definition

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