[solved]-Question 4 Counting Problems 6 Marks Questions Answer Must Consist Formula Terms Number Ve Q39082755

Question 4: Counting Problems [6 marks] For each of the questions below, your answer must consist of a formula in terms of the number of vertices n, along with a brief but concise justification of its correctness. Answers without sufficient justification will receive no marks. (a) We know that the maximum number of possible edges in a graph on n vertices is In non – 1) Derive a formula which counts the number of possible graphs on n vertices (with no restrictions whatsoever on the structure of the graph, besides that it has n vertices and is an undirected simple graph). (b) Suppose G is a graph on n > 4 vertices with exactly four connected components. Derive a formula for the maximum number of edges in G. (C) Suppose G is a directed acyclic graph with exactly k minimum vertices. Derive a formula in terms of n and k) for the minimum number of directed edges in G. Show transcribed image text Question 4: Counting Problems [6 marks] For each of the questions below, your answer must consist of a formula in terms of the number of vertices n, along with a brief but concise justification of its correctness. Answers without sufficient justification will receive no marks. (a) We know that the maximum number of possible edges in a graph on n vertices is In non – 1) Derive a formula which counts the number of possible graphs on n vertices (with no restrictions whatsoever on the structure of the graph, besides that it has n vertices and is an undirected simple graph). (b) Suppose G is a graph on n > 4 vertices with exactly four connected components. Derive a formula for the maximum number of edges in G. (C) Suppose G is a directed acyclic graph with exactly k minimum vertices. Derive a formula in terms of n and k) for the minimum number of directed edges in G.

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Answer to Question 4: Counting Problems [6 marks] For each of the questions below, your answer must consist of a formula in terms … . . .