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March 28, 2017

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Let G be a graph with vertex set V = {v1, v2, v3, v4, v5}.

A. Is it possible for the degrees of the vertices to be 3, 6, 2, 1, 5, respectively? Why or why not?

B. If the degrees of the vertices are 1, 2, 3, 4, 6, respectively, how many edges are in G?

C. If the degrees of the vertices are 5, 1, 0, 6, 2, respectively, does G have an Eulerian path? Why or why not?

D. If the degrees of the vertices are 1, 2, 1, 3, 1, respectively, is G a tree? Why or why not?

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