Question

quiz 11
version a\t\t\tstudent id number: 9______

1. (5 points) does the graph to the right

have an eulerian circuit, an eulerian
walk, or neither?
\t○ an eulerian circuit.
\t○ an eulerian walk.
\t○ neither of the above.

graph with nodes a, b, c, d, e, f, g and edges between them

Explanation:

Step1: Recall Eulerian circuit and walk conditions

An Eulerian circuit exists if all vertices have even degrees. An Eulerian walk exists if exactly two vertices have odd degrees.

Step2: Calculate vertex degrees

• Degree of \(A\): \(3\) (edges \(AB\), \(AE\), \(AG\))
• Degree of \(B\): \(3\) (edges \(AB\), \(BC\), \(BD\))
• Degree of \(C\): \(2\) (edges \(BC\), \(CD\))
• Degree of \(D\): \(3\) (edges \(BD\), \(CD\), \(DG\))
• Degree of \(E\): \(2\) (edges \(AE\), \(EG\))
• Degree of \(F\): \(1\) (edge \(FG\))
• Degree of \(G\): \(4\) (edges \(AG\), \(EG\), \(DG\), \(FG\))

Vertices \(A\), \(B\), \(D\) have odd degrees (\(3\)), and vertex \(F\) has degree \(1\) (odd). There are more than two vertices with odd degrees.

Answer:

Neither of the above.