Question

Does graph A have an Euler path or an Euler circuit? Explain how you know.

Answer 1

Answer:

• Graph A: neither an Euler path nor an Euler circuit
• Graph B: both an Euler path and an Euler circuit
• Graph C: both an Euler path and an Euler circuit

Step-by-step explanation:

A non-directed graph will have an Euler circuit if all vertices have even degree. It will have an Euler path if it has an Euler circuit or if it has two vertices with odd degree (where the path can start and end).

Graph A

  4 of the 5 vertices have odd degree. No Euler path, no Euler circuit.

Graph B

  All 6 vertices have degree 4. This graph has an Euler path and an Euler circuit.

Graph C

  5 of 6 vertices have degree 4, the remaining one has degree 2. This graph has an Euler path and an Euler circuit.