# a4 - n 1’s and n 0’s where 2 vertices(strings are...

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MATH 239 Assignment 4 This assignment is due at noon on Friday, June 22, 2007, in the drop boxes opposite the Tutorial Centre, MC 4067. 1. Solve the linear homogeneous recurrence relation c n - 7 c n - 1 + 16 c n - 2 - 12 c n - 3 = 0 n 3 with initial conditions c 0 = - 1 , c 1 = 5, and c 2 = 23. 2. Solve the nonhomogeneous linear recurrence relation a n - 5 a n - 1 - a n - 2 + 5 a n - 3 = 96 - 32 n with initial conditions a 0 = 4 , a 1 = 3, and a 2 = 30. 3. Determine which pairs of graphs are isomorphic, and which pairs are not. Justify your answer. S D c d f 1 4 H G F E C B A a b e g h 2 3 5 6 7 8 Graph Graph Graph U T 4. Let A 2 n be the graph whose vertices are all binary strings with
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Unformatted text preview: n 1’s and n 0’s, where 2 vertices (strings) are adjacent if and only if they diﬀer in exactly two positions. (a) Draw graphs A 2 and A 4 . (b) Determine the number of vertices and edges in A 2 n . (c) Is A 2 n connected? Justify your claim. 5. (a) Let G be a graph with p vertices. Show that if every vertex has degree at least b p 2 c , then G is connected. (b) Can this result be strengthened; that is, does it still hold if every vertex has degree at least b p 2 c -1? 1...
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