Unformatted text preview: D. The only such path is ABCDE of length 27: d(l, 5) = 27. The value of d(l, 6) is the length of a shortest path from A to F via A, B, C, D. There is no such path, so d(l, 6) is still 00. The value of d(3, 4) is 8. The value of d(8, 5) is the length of a shortest path from H to E via A, B, C, D. The shortest such path is HBCDE: d(8, 5) = 24. (c) [BB] The initial value of d(2, 5) is 00 since BE is not an edge. After k = 1,2, ... , 10, the values of d(2, 5) are 00, 00, 00, 20, 20, 20, 20, 20, 18, 17. 18. (a) These are the shortest distances from V7 to each of VI, ... ,Vs; namely, 4, 3, 1,2, 3, 3, 0, 4 (b) d(1,2) = 1; d(3, 4) = 1; d(2, 5) = 4; d(8, 6) = 10. (c) 00,00,00,12,10,5,5,5,5 19. It certainly does! In the graph at the right, with i = 1 and j = 2, the algorithm finds that the smallest value of d(l, k) + d(k, 2) is 4 (because at this stage, d(1,3) = d(4, 2) = 00) and this value never changes....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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