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 fleurys 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 \(A\): \(2\) (even)
• Degree of \(B\): \(2\) (even)
• Degree of \(C\): \(2\) (even)
• Degree of \(D\): \(4\) (even)
• Degree of \(E\): \(2\) (even)
• Degree of \(F\): \(1\) (odd)
• Degree of \(O\): \(1\) (odd)

Since there are exactly two vertices (\(F\) and \(O\)) with odd degrees.

Answer:

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