1. For each of the five descriptions below, draw (NEATLY), if possible, an undirected graph G that satisfies the conditions. If it's impossible, provide a proof of the impossibility. G is simple and has five vertices, two of which have degree 3 and three vertices of degree 2 a) b) G has ten edges and each vertex has degree 5 e) G is simple and has six vertices and thirteen edges d) G is simple, has six vertices, thirteen edges, and is bipartite 2. Suppose G is an undirected simple graph with n vertices, one of which has degree 0 and one of degree 1 and one of degree 2 and and one of degree n - 1. For which values of n is this possible? Justify your answer 3. Draw a simple connected graph G which has a cut vertex, and for every vertex v in G, deg(v) 3. If it is impossible then prove why. 4. Are any of these degree sequences graphic? If you determine that the sequence is graphic, draw a graph with the given degree sequence. If you determine that the sequence is not graphic, prove it. a) 55443 22 b) 6644 422 c) 666666 d) 6666666 1. For each of the five descriptions below, draw (NEATLY), if possible, an undirected graph G that satisfies the conditions. If it's impossible, provide a proof of the impossibility. G is simple and has five vertices, two of which have degree 3 and three vertices of degree 2 a) b) G has ten edges and each vertex has degree 5 e) G is simple and has six vertices and thirteen edges d) G is simple, has six vertices, thirteen edges, and is bipartite 2. Suppose G is an undirected simple graph with n vertices, one of which has degree 0 and one of degree 1 and one of degree 2 and and one of degree n - 1. For which values of n is this possible? Justify your answer 3. Draw a simple connected graph G which has a cut vertex, and for every vertex v in G, deg(v) 3. If it is impossible then prove why. 4. Are any of these degree sequences graphic? If you determine that the sequence is graphic, draw a graph with the given degree sequence. If you determine that the sequence is not graphic, prove it. a) 55443 22 b) 6644 422 c) 666666 d) 6666666