Discrete Mathematics - 21137

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  • Due on: Wed 31 Jul, 2013 (09:39pm)
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For the two questions that follow only, determine whether the binary relation is reflexive, symmetric, antisymmetric, and/or transitive. 1. The relation R on Z where aRb means a2 = b2. 2. The relation R on A = {x,y,z} where R = {(x,x), (y,z), (z,y)}. 3. Give a relation on {1,2} that is symmetric and transitive, but not reflexive? 4. Suppose ?A? = n. Find the number of binary relations on A. For the next five questions, fill in the blanks. 5. Kn has _____ edges and _____ vertices. 6. The length of the longest simple circuit in K4,10 is ______. 7. There are _____ non-isomorphic simple undirected graphs with 5 vertices and 3 edges. 8. Every Euler circuit for K9 has length ________. 9. The edge-chromatic number for K2,5 = _________. 10. In K5 find the number of paths of length 2 between every pair of vertices. 11. In K3,3 let a and b be any two adjacent vertices. Find the number of paths between a and b of length 4. 12. Find the vertex-chromatic number for C7. 13. Find the region-chromatic number for C7. 14. Find the vertex-chromatic number for Gm,n.

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