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For each exercise below, assume the graph is a simple graph. Given vertices A, B, C and D, how many triangles can be drawn using
For each exercise below, assume the graph is a simple graph. Given vertices A, B, C and D, how many triangles can be drawn using them? List the triangles. Give a formula for the number of triangles that can be drawn from n vertices, where n greaterthanorequalto 3. How many edges does K_5, the complete graph on five vertices, have? Give a formula for the number of edges that K_n, the complete graph on n vertices, has. An r-regular graph of order n, denoted K_n, r, is a graph with n vertices each of which has r neighbors. Draw a connected K_6, 3, a connected 3-regular graph of order six. How many edges does the graph have? Explain why it is impossible to have a 3-regular graph of order 5. Give a formula in terms of n and r for the number of edges in a K_n, r graph
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