Discrete Mathematics with Graph Theory (3rd Edition) 293

# Discrete Mathematics with Graph Theory (3rd Edition) 293 -...

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Chapter 10 24. A is given the label (-,0). Next C is labelled (A, 2), then D is labelled (A, 4) and B is (A, 5). Then G is labelled (D, 6) and F is (C, 7) Then E is labelled (G,8) and H is (F,9) or (G, 9). Finally, I is labelled (F, 11). These labels give the required lengths. One shortest path from A to H is AC F H; ADG H is another, since H could also have been labelled (G, 9). 25. First, A is given the label 0 and all other vertices are given temporary labels of 00. Next, B, C, D and E are given temporary labels of 5,2,4 and 10, respectively, and 2 becomes the permanent label on C. Now the temporary label on E is decreased to 9 while F is given a temporary label of 7. So D gets the next permanent label, 4. Now G acquires a temporary label of 6 (E's temporary label of 9 does not change) and B gets the next permanent label, 5. No new temporary labels are assigned, so the next permanent label is 6 on G. Now E's temporary label is decreased to 8, while H gets a temporary label of 9. 291
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