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# hw9.5 - contradiction Question 8 The 2-dimensional torus T...

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ECE 103 Discrete Math for Engineers University of Waterloo Spring 2010 Instructors: Koray Karabina, Ashwin Nayak Suggested problems (not to be submitted), July 30, 2010 RSA Cryptosystem Question 1. Pages 104–105, excercises 1 (using the recursive powering algorithm), 2 to 6. Counting and probability Question 2. Pages 130–135, exercises 1 to 16, 18, 19 (first part), 20 to 31, 33, 35 to 38, 40 to 43. Graphs Question 3. Page 173–174, all exercises. Question 4. Page 179–180, exercises 1, 4, 5, 7. Question 5. Page 185, all exercises. Question 6. Page 188–189, all exercises. Question 7. Page 191, all exercises. (2 is challenging, assume the graph has a cycle, and try to get a
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Unformatted text preview: contradiction.) Question 8. The 2-dimensional torus T n is a graph with n 2 vertices, and 2 n 2 edges when n ≥ 3. (It has no edges when n = 1, and 4 edges when n = 2.) Its vertices are labeled with pairs ( x, y ), where x, y ∈ { , 1 , . . . , n-1 } . Its edges are between pairs ( x, y ) and ( u, v ) such that either u ≡ x (mod n ) , v ≡ y + 1 (mod n ) or u ≡ x +1 (mod n ) , v ≡ y (mod n ). (This graph may be drawn on a donut shaped surface, called a torus , such that no edges intersect.) Describe an Euler(ian) tour in T n . Does T n have a Hamilton(ian) cycle? 1...
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