SOLUTION: Is it D? I chose D as my answer, but my assignment said it was wrong. Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph? A. ADBCA

Algebra ->  Sequences-and-series -> SOLUTION: Is it D? I chose D as my answer, but my assignment said it was wrong. Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph? A. ADBCA       Log On


   

Question 1161589: Is it D? I chose D as my answer, but my assignment said it was wrong.
Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph?
A. ADBCA
B. ABCDA
C. ACBDA
D. all of the above

The graph for the question and the question itself are in the question here: https://i.imgur.com/TCEqxzO.png
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Yes, answer D.

They all start and end at the same vertex, and they all visit each other vertex exactly once.

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I saw another post of this same problem where the reader said he was told that answer D was wrong.

It would only be wrong if the intersection of edges AC and BD is a vertex of the graph.

However, it is customary in graph theory to label ALL vertices in a graph; so an unlabeled point where two edges cross is not considered a vertex.

So D is the correct answer.