Use Euler\'s theorem to determine whether the graph has an Euler circuit. If not

Question

Use Euler's theorem to determine whether the graph has an Euler circuit. If not, explain why not If the graph does have an Euler circuit, use Fleury's algorithm to find an Euler circuit for the graph. Does the graph have an Euler circuit? A. No, because all vertices have even degree B. No, because some vertices have odd degree O C. Yes, because all vertices have even degree if the graph does have an Euler circult,use Fleury's algorithm to find an Euler circuit for the graph 0 A. The circuit AC+B+D+A is an Euler circuit O B. The circuit DACBD is an Euler circuit O C. The graph does not have an Euler circuit

Explanation / Answer

Observe that there are 3 edges connected to every vertex in the graph except vertex E.

Therefore, the graph has vertices A,B,C and D with odd degree.

And so there is not Euler circuit.

The answer is:

B. No, because some vertices have odd degree.

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