Unformatted text preview: B n , n ≥ 1. (b) Determine the number of edges in B n , n ≥ 1. (c) Determine the values of n ≥ 1 for which B n is connected. 3. Suppose that G is a graph in which the minimum vertex degree is equal to d , for some d ≥ 2. (a) Prove that G has a path of length at least d . (b) Prove that G has a cycle of length at least d + 1. 4. If H has p vertices, p ≥ 1, and every vertex in H has degree greater than or equal to 1 2 p , prove that H is connected. 5. A quartic tree is a tree whose vertices have degrees 1 or 4 only. Prove that every quartic tree with m vertices of degree 4 has a total of 3 m + 2 vertices, for m ≥ 0....
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 Fall '09
 M.PEI
 Graph Theory, Sets, Vertex, vertices

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