For each exercise below, assume the graph is a simple graph. Given vertices A, B

Question

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.

Explanation / Answer

A) we have to choose 3 vertices out of 4 hence we can apply 4C3 which is equal to 4.

B)The no of edges in kn = n(n 1)/2

Hence the no of edges in K5 = 10

C)It will have 18 edges as the 6 vertices are connected to the 3 vertices.

D)it is impossible as there are 3 edges only so the max order can be of 3 and not more

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