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Unformatted text preview: ITI 111 – Spring 2011 Homework 10 Reasoning about arbitrary graphs 1. Suppose we have 4 boxes: How many total different ways are there to put 4 beans in those 4 boxes? a. ( ) b. ( ¡¢ ) c. ( £ ) d. ( ¤ £ ) 2. What does your answer to 1 evaluate to? a. 12870 b. 35 c. 1 d. 70 3. In class we learned how we can apply the above principle to determine how many graphs can be drawn using v vertices and e edges. First, we need to figure out how many “boxes” [in other words: places to put edges] there are. In order to do this, we: a. Calculate the triangular number at v : T v b. Calculate the number of combinations of e and v : ( ¥ ¦ ) c. Calculate the square of v : v 2 d. Realize that if there are v vertices then there are v boxes and simply use: v 4. Suppose we have a graph with 3 vertices. How many “boxes” [places to put edges] are there? a. 3 b. 6 c. 9 d. We can‟t say because we don‟t know how many edges there are 5. If we have a graph with 3 vertices and 5 edges, how do we calculate how many possible ways there are to draw this graph? a.a....
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