Eulerian Path Degree Test

00:00 3 marks

  • Build Confidence
  • HL
  • Tier 2
  • Graph theory
  • Eulerian paths
  • Parity of vertex degree

Consider a connected graph with 7 vertices having the following degrees: 3, 2, 2, 2, 2, 2, 2. Determine whether this graph can have an Eulerian path.

Hint Hint

Hint

Recall that for an Eulerian path to exist in a connected graph, the number of vertices with odd degree must be either 0 or 2.

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Complete Answer

No, the graph does not have an Eulerian path because it has exactly 1 odd-degree vertex, which does not satisfy the necessary condition of having 0 or 2 odd-degree vertices.

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