Consider the following graph.
• V(G) = {v1, v2, v3, v4},
• e(G) = {e1, e2, e3, e4, e5},
• E(G) = {(e1, [v1, v2]), (e2, [v1, v2]), (e3, [v2, v3]), (e4, [v3, v4]), (e5, [v3, v4])}
Draw a picture of the graph on scratch paper to help you answer the following four questions.
1. What is the degree of the graph G?
2. How many simple circuits can be identified in graph G?
3. How many walks of length 2 are there from v2 to v4?
4. How many edges are in a spanning tree for graph G?
Hint: For Q3, use the graph's adjacency matrix and Theorem 10.2.2 on page 709 of the textbook.