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

A graph has an Euler circuit if all vertices have even degrees. A graph has an Euler path if exactly two vertices have odd degrees.

Step2: Calculate vertex degrees

• Degree of \(A\): \(1\) (odd)
• Degree of \(B\): \(2\) (even)
• Degree of \(C\): \(3\) (odd)
• Degree of \(D\): \(2\) (even)
• Degree of \(E\): \(3\) (odd)
• Degree of \(F\): \(1\) (odd)

Since there are four vertices (\(A\), \(C\), \(E\), \(F\)) with odd degrees.

Answer:

The graph has neither an Euler path nor an Euler circuit.