(a)  Give the definition of an isomorphism from a graph G to a graph H. (b)  Consider the graphs G and H below. Are G and H isomorphic? • If yes, give an isomorphism from G to H. You don’t need to prove that it is an isomorphism. • If no, explain why. If you claim that a graph does not have a certain feature, you must demonstrate that concretely.   (c)  Consider the degree sequence (1, 2, 4, 4, 5). For each of the following, if the answer is yes, draw an example. If the answer is no, explain why. (i) Does there exist a graph with this degree sequence? (ii) Does there exist a simple graph with this degree sequence?

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