Final answer:
In a graph with 6 vertices, all of degree 5, you can find the number of edges using the Handshaking Lemma. The graph with 9 vertices and 36 edges has a degree of 8. The graph with 36 edges and vertices all of degree 6 has 12 vertices.
Step-by-step explanation:
In a graph with 6 vertices, all of degree 5, we can use the Handshaking Lemma to find the number of edges. The Handshaking Lemma states that the sum of the degrees of all vertices in a graph is twice the number of edges. So, if the graph has 6 vertices, all of degree 5, the sum of the degrees is 6 * 5 = 30. Therefore, the number of edges is 30 / 2 = 15.
In the second part of the question, we are given that the graph has 9 vertices, all of degree ? and 36 edges. We can use the same formula to find the degree: 2 * 36 = 9 * ?. Solving for ?, we find that the degree is 8.
Finally, in the third part of the question, we are given that the graph has ? vertices, all of degree 6, and 36 edges. Using the same formula, we can find the number of vertices: 2 * 36 = ? * 6. Solving for ?, we find that the graph has 12 vertices.