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Discrete Mathematics with Graph Theory (3rd Edition) 285

Discrete Mathematics with Graph Theory (3rd Edition) 285 -...

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Section 10.4 283 Va 3 V6 3 VlO 3 VIa E @ VI6 3 Vs 2 Vg G) o 10. [BB] The shortest path has length 13. 11. The shortest path has length 13 and is shown on the graph. @1 12. [BB] In each case the answer is yes, if A and E were in different components of a graph which was not connected. 13. The idea was interesting, but I don't think it works. Here is a graph where the "new improved" algorithm could give 11 for the distance from A to E by making a bad choice of V2. 14. (a) The graph is not Hamiltonian.
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Unformatted text preview: CD vI=A~~a=E ~ vii) (b) Both edges incident with vertices E, F, G and H must be in any circuit, that is, AE, DE, BF, DF, AG, DG, GH andDH. Vertices B andG appear only once among these edges, so if they are to be part of a circuit, additional edges incident with B and G must appear. The most economical way to do this is simply to add edge BG, of weight 2, obtaining the circuit AEDFBGHDGA of total weight 25. (c) No! For instance, ABGH DF DEDGA provides a route of length 23....
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