Question

examine the graph to the right.
a. determine whether the graph has an euler path, an euler circuit, or neither
b. 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
a. the graph has an euler circuit.
b. the graph has an euler path (but not an euler circuit)
c. the graph has neither an euler path nor an euler circuit

Explanation:

Step1: Recall Euler's theorem

A graph has an Euler circuit if and only if all vertices have even degrees. A graph has an Euler path (but not a circuit) if and only if exactly two vertices have odd degrees.

Step2: Calculate vertex degrees

• Degree of \(A\): \(4\) (even).
• Degree of \(B\): \(4\) (even).
• Degree of \(C\): \(2\) (even).
• Degree of \(D\): \(2\) (even).

Since all vertices have even degrees, the graph satisfies the condition for an Euler circuit.

Answer:

A. The graph has an Euler circuit