T301-1-09 - AMS 301.1 a i e g h b c d 1 9 5 f FIRST TEST A...

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AMS 301.1 FIRST TEST A Fall, 2009 Prof. Tucker 1. Are these two graphs isomorphic? Give the isomorphism or explain why none exists. a 1 b 6 c 3 d 8 e 5 f 2 g 7 h 4 i 9 2. Find a lower bound on the minimal-cost 1 2 3 4 traveling salesperson tour for the table 1 9 3 7 a b c d e f g on the right (using the method in the text). 2 7 7 3 a 0 1 0 0 0 1 1 Suggest a good entry on which to branch. 3 5 6 4 b 1 0 1 0 0 0 0 What is the new bound if you do not use 4 7 8 5 c 0 1 0 0 0 1 0 this entry? If you do use this entry? d 0 0 0 0 0 1 0 e 0 0 0 0 0 0 1 3. Is the graph with the adjacency matrix on the right connected? Test by f 1 0 1 1 0 0 0 trying to build a spanning tree found by a depth-first search starting at a. g 1 0 0 0 1 0 0 4. A convention of actuaries will have rooms available in eight hotels. There are 200 actuaries and because of personality conflicts, various pairs of actuaries must be put in different hotels. The organizers wonder whether
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