a) The graph H has a node set {a, b, c, d, e} and nine edges,...

 

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a) The graph H has a node set {a, b, c, d, e} and nine edges, consisting of all possible edges except (c, e). i. Are all graphs with five nodes and nine edges isomorphic to H? Justify your answer. Is H a planar graph? Prove your answer. ii. b) Construct the labelled tree which has the Prfer code (6, 7, 6, 4, 3). c) Let I' be a tree, all of whose vertices have degree either 1 or 3. Such a tree is called trivalent and often occurs in evolutionary biology. If I has n leaves, show that it has n - 2 vertices of degree 3. Page 1 of 2 a) The graph H has a node set {a, b, c, d, e} and nine edges, consisting of all possible edges except (c, e). i. Are all graphs with five nodes and nine edges isomorphic to H? Justify your answer. Is H a planar graph? Prove your answer. ii. b) Construct the labelled tree which has the Prfer code (6, 7, 6, 4, 3). c) Let I' be a tree, all of whose vertices have degree either 1 or 3. Such a tree is called trivalent and often occurs in evolutionary biology. If I has n leaves, show that it has n - 2 vertices of degree 3. Page 1 of 2