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Which vertices are adjacent to form edges of this

Question: 1. How many possible orderings of A, B, C, D are there?

2. What is the connection of this situation to graph theory? That is, there is a graph here, so

(a) What are the vertices of this graph? (How many will there be?)

(b) Which vertices are adjacent to form edges of this graph?

(d) What structure do you seek in this graph?

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