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Discrete Mathematics with Graph Theory (3rd Edition) 307

Discrete Mathematics with Graph Theory (3rd Edition) 307 -...

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Section 11.2 305 (b) Max. no. of arcs 1 2 3 4 5 V2 3,VI 3,VI 3,VI 3,VI 3,VI V3 00 8,V2 6,V6 6,V6 6,V6 V4 00 00 1l,v3 9,V3 9,V3 Vertices V5 00 00 00 17, VlO 1O,v4 V6 00 4,V2 4,V2 4,V2 4,V2 V7 00 00 13,v3 9,vg 9,vg Vs 6,VI 6,VI 6,VI 6,VI 6,VI Vg 00 14,vs 7,V6 7,V6 7,V6 VlO 00 00 16,vg 9,vg 9,vg 22. (a) [BB] Max. no. of arcs 1 2 3 4 5 6 V2 1,VI 1, VI 1,VI 1,VI 1,VI 1,VI V3 8,VI 2,V2 2,V2 2,V2 2,V2 2,V2 V4 00 1l,v3 5,V3 4,V5 4,V5 4,V5 V5 00 4,V2 3,V3 3,V3 3,V3 3,V3 V6 7,VI 7,VI 7,VI 6,V5 6,V5 6,V5 (b) Max. no. of arcs 1 2 3 4 5 6 V2 4,VI 2,V4 2,V4 2,V4 2,V4 2,V4 V3 00 5,V2 3,V2 3,V2 3,V2 3,V2 V4 1,VI 1,VI 1, VI 1,VI 1,VI 1, VI V5 7,VI 7, VI 6,V3 4,V3 4,V3 4,V3 V6 8,VI 7,V4 7,V4 6,V3 5,V5 5,V5 23. [BB] Bellman-Ford works fine on undirected graphs without negative edges.
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Unformatted text preview: It wouldn't make sense to apply Bellman-Ford to an undirected graph with a negative edge weight, since any walk could be shortened by passing up and down that edge as often as desired. 24. (a) [BB] Dijkstra incorrectly determines that the length of a shortest path to V2 is 1. Dijkstra does not always work when applied to digraphs which have arcs of negative weight. (b) [BB] No shortest path algorithm will work. There is a negative weight cycle, hence no shortest dis-tance to V2, for example. 25. (a) Because of the negative weight arcs, Dijkstra's algorithm does not find the correct shortest dis-tances to C, D, E, and F, these being 3, 4, 4 and 1, respectively. (b) Bellman-Ford would work just fine, however, because there are no negative weight cycles....
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