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# 222a5 - 3 Let S = 1 2 3 4 5 Let G = V E be the graph where...

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MATH 222 FALL 2011, Assignment Five (due Wednesday, Nov. 16 in class before the lecture begins) Show yourwork clearly. Illegible or disorganized solutions will receive no credit. 1. Use generating functions to solve the following recurrence relations with initial con- ditions. (a) a k - a k - 1 = 2 k + 1 , k 1 , a 0 = 1; [3] (b) a k - 2 a k - 1 = 2 k , k 1 , a 0 = 1. [3] 2. Suppose that graph G has 17 edges and every vertex of G has degree at least 3. (a) What is the maximum possible number of vertices that G can have? [2] (b) Construct such a graph with the maximum possible number of vertices.
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Unformatted text preview: 3. Let S = { 1 , 2 , 3 , 4 , 5 } . Let G = ( V, E ) be the graph where V consists of all 2-element subsets of S , and two vertices are adjacent in G if and only if the two corresponding sets are disjoint (e.g., the two vertices corresponding to { 1 , 3 } , { 2 , 5 } are adjacent, and the two vertices corresponding to { 1 , 3 } , { 3 , 5 } are not adjacent). (a) Draw the graph G and show that it is isomorphic to the Petersen graph; [2] (b) Find a trail in G that contains as many edges as possible. [2]...
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