Discrete math 2
Discrete math 2 test 1 I. Graph theory 1. Create the adjacency matrix of the following graph: 2 pts 2. neither. State whether the graph has an Euler circuit, an Euler path, or a. 1 pt. b. 1 pt. c. 1 pt. 3. Draw a tournament with five players, in which player A beats everyone but E, B beats everyone but A, C beats D and E beats everyone but B. 2 pts. 4. Create a Hamiltonian circuit for a 4-dimensional hypercube 2 pts. 5. Use Dijkstra’s algorithm to build a shortest path tree. Use vertex P as starting vertex. 3 pts. 6. Stable matching. There are 5 boys (1,2,3,4,5) and 5 girls (A,B,C.D,E). Match the boys and girls in a good way (stable matchings) starting with boys. Preference list for boys 1 2 3 4 5 A,D,B,C,E A,D,B,C,E B,E,D,A,C B,A,D,E,C D,C,B,A,E Preference list for girls A B C D E 1,5,3,2,4 5,4,3,1,2 3,1,4,2,5 3,1,2,5,4 1,2,4,5,3 2 2pts. 7. Bipartite matching. Job Assignment Problem. There are 6 persons (A,B,C,D,E,F) and 6 jobs (!,2,3,4,5,6). Preferences are presented in the following matrix. 1 v v A B C D E F 2 v v v 3 v 4 5 6 v v v v v v v v v v v v Find an assignment so that all jobs are taken care of, while everyone is responsible for at most one job? 2 pts. 8. Graph coloring. Determine the chromatic number χ(G) of the following graphs: a. 1 pt. b. 1 pt. c. 1 pt. 3 9. Scheduling using conflict graphs. Create a schedule for the following flight plan using minimal number of gates. Flight Time 132 115 57 217 301 79 2 pts. 10. Draw a planar graph with 6 vertexes and 10 edges. 2 pts. 11. Representing relations. Let R = {(1,3), (2, 1), (2,2), (3, 1), (3, 2), (3,3}. Represent R: a) Using zero-one matrix; 1 pt. b) Using digraph. 1 pt. 12. Combining relations. Let: D = {(1, 4), (2, 3), (3, 2), (4, 1)} S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)} Combine: a. DUS 1 pt. b. D 1 pt. S 13. Perform the following modular operations: a. 47+32 mod 7 1 pt. b. 35*28 mod 11 1 pt. 14. Find φ(n) for: 4 a. n = 35 1 pt. b. n = 77 1 pt. c. n = 143 1 pt. 15. Find the multiplicative inverse mod n: 8-1 mod 21 2 pt. 16. Modular exponentiation: 6726 mod 21 2 pt. Rules for estimation 1. The max score is 36 points 2. The distribution of grades is: a) 6 – over 30 points b) 5 – between 25 and 30 points c) 4 – between 19 and 24 points d) 3 – between 13 and 18 points e) 2 – under 13 points 5
Collepals.com Plagiarism Free Papers
Are you looking for custom essay writing service or even dissertation writing services? Just request for our write my paper service, and we'll match you with the best essay writer in your subject! With an exceptional team of professional academic experts in a wide range of subjects, we can guarantee you an unrivaled quality of custom-written papers.
Get ZERO PLAGIARISM, HUMAN WRITTEN ESSAYS
Why Hire Collepals.com writers to do your paper?
Quality- We are experienced and have access to ample research materials.
We write plagiarism Free Content
Confidential- We never share or sell your personal information to third parties.
Support-Chat with us today! We are always waiting to answer all your questions.
