Discrete Mathematics with Graph Theory (3rd Edition) 361

Discrete - Chapter 12 18 A canonical ordering is L C K J I H G M D E F A B(a The table shows the lengths o f shortest paths and predecessor

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Chapter 12 359 18. A canonical ordering is L, C, K, J, I, H, G, M, D, E, F, A, B. (a) The table shows the lengths of shortest paths and predecessor vertices when root is Vo. L C K J I H G M D E F A B dt 0 1 2 3 1 1 2 3 2 3 5 4 3 Pt -1 L C K L L H L L D M K C (b) Here are the lengths and predecessor vertices when root is VI. L C K J I H G M D E F A B dt 00 0 1 2 3 4 5 6 3 4 6 3 2 Pt -1 -1 C K K I H H C D E K C 19. (a) The final backtracking is 16,15,14,13,12,11,7,6,5,4,3,2,1. The edges on the resulting span- ning tree are darkened. 2 1 2 16 15 10 3 4 14 8 7 9 6 5 13 7 11 8 12 (b) The final backtracking is 8, 1. The edges on the resulting spanning tree are darkened. 20. The graph in (a) is strongly connected; the one in (b) is not. 2 1 2 16 15 (a) 10 3 4 14 (b) 9 6 5 13 8 7 11 12 7 21. If V is incident with e, then we can start a depth-first search at v and select edge e first. So v and e would be in the eventual spanning tree. So assume e = UW, where neither of the end vertices u and w
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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.

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