ds-t3(1)

# 1 1 0 1 0 1 m r 1 0 1 m s 1 1 0 0 1 0 1 0 1 a if we

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1 1 0 1 0 1 M R = 1 0 1 M S = 1 1 0 0 1 0 1 0 1 (a) If we assume that the matrices were constructed using the order listed above for the set A, then R = (b) What is the matrix representing R S? M R S = (c) Construct the digraph representing S in the space below. 4. (10 pts.) (a) Using the prefix code a:001, b:0001, e:1, r:0000, s:0100, t:011, and x:01010, decode the following bit string: 0111001000100100000100 (b) Construct the ordered rooted binary tree representing the following expression: (C - (A B)) = ((C - A) (C - B))

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TEST-3/MAD2104 Page 3 of 4 5. (15 pts.) (a) Draw a directed graph G 1 whose adjacency matrix is 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 . (b) Now draw an undirected graph G 2 which is represented by the adjacency matrix in part (a) of this problem. (c) Is G 2 = (V 2 ,E 2 ), above, isomorphic to the simple graph G 3 = (V 3 ,E 3 ) given below? Either display an isomorphism f:V 2 -> V 3 or very briefly explain why there is no such function by revealing an invariant that one graph has that the other doesn’t.
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• Fall '08
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• Graph Theory, pts, Binary relation, Tree traversal, Nested set model

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