Question

determine whether the graph has an euler path, an euler circuit, or neither
if the graph has an euler path or circuit, use trial and error or fleury’s algorithm to find
one.

a. choose the correct answer below
○ the graph has an euler path (but not an euler circuit)
○ the graph has an euler circuit.
○ the graph has neither an euler path nor an euler circuit.

Explanation:

Step1: Recall Euler's theorem conditions

An Euler circuit exists if all vertices have even degree. An Euler path exists if exactly two vertices have odd degree.

Step2: Calculate vertex degrees

• Degree of \(A\): \(1\) (odd)
• Degree of \(B\): \(1\) (odd)
• Degree of \(C\): \(1\) (even)
• Degree of \(D\): \(4\) (even)
• Degree of \(E\): \(1\) (even)
• Degree of \(F\): \(1\) (even)
• Degree of \(G\): \(1\) (even)

Since there are exactly two vertices (\(A\) and \(B\)) with odd degree.

Answer:

The graph has an Euler path (but not an Euler circuit)